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CBSE CLASS 10 · POLYNOMIALS · 1 MARK EACH

CBSE Class 10 Polynomials MCQs
(2022–2026)

Polynomials 2-Mark Questions with Answers →

Practise 27 selected MCQs from board examinations and official CBSE sample papers with answers and compact worked solutions. Questions from 2022–2026 are labelled by Basic or Standard, examination, paper code and question number.

The 2022 exam cycle includes 2021–22 Term 1, held on 4 December 2021. These questions are labelled by session and examination date.

Solutions prepared by Team TutorVertex

Practise 7 Polynomials Assertion–Reason previous-year questions →

Zeroes & polynomial values

QUESTION 1 · Easy · 1 MARK

CBSE 2023 · Standard · Main · 30/2/1 · Q14

Find the zeroes of x² + 4x + 3.

A. 1, 3 B. −1, 3 C. 1, −3 D. −1, −3

Show Answer & Explanation

x² + 4x + 3 = (x + 1)(x + 3)

x + 1 = 0 or x + 3 = 0

Zeroes: −1 and −3

Correct answer: D — −1, −3

Common trap: A factor x + 3 gives the zero −3.

Why the other choices are incorrect

A: both signs are reversed. B and C: one root has the wrong sign; their sums are not −4.

Source: CBSE 2023 · Standard · Main · 30/2/1 · Q14
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 2 · Easy · 1 MARK

CBSE 2023 · Basic · Supplementary · 430/C/1 · Q8

What is the degree of the zero polynomial?

A. 0 B. 1 C. any real number D. not defined

Show Answer & Explanation

Every coefficient in the zero polynomial is 0.

There is no highest power with a non-zero coefficient.

Its degree is not defined.

Correct answer: D — not defined

Common trap: A non-zero constant has degree 0; the zero polynomial is different.

Why the other choices are incorrect

A: applies to a non-zero constant. B: requires a non-zero x term. C: the degree is undefined rather than an arbitrary real number.

Source: CBSE 2023 · Basic · Supplementary · 430/C/1 · Q8
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 3 · Easy · 1 MARK

CBSE 2024 · Standard · Main · 30/3/1 · Q6

Find the zeroes of 2x² − 3x − 9.

A. 3, −3/2 B. −3, −3/2 C. −3, 3/2 D. 3, 3/2

Show Answer & Explanation

2x² − 3x − 9 = 2x² − 6x + 3x − 9

= (x − 3)(2x + 3)

Zeroes: 3 and −3/2

Correct answer: A — 3, −3/2

Common trap: The factor 2x + 3 gives x = −3/2.

Why the other choices are incorrect

B and C: −3 is not a zero. D: changes the sign of the second zero, giving a positive product instead of −9/2.

Source: CBSE 2024 · Standard · Main · 30/3/1 · Q6
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 4 · Easy · 1 MARK

CBSE 2024 · Standard · Main · 30/4/1 · Q3

For p(x) = x² − 5x + 6, find p(1) + p(4).

A. 0 B. 4 C. 2 D. −4

Show Answer & Explanation

p(1) = 1 − 5 + 6 = 2

p(4) = 16 − 20 + 6 = 2

p(1) + p(4) = 2 + 2 = 4

Correct answer: B — 4

Common trap: Substitute into the whole polynomial each time.

Why the other choices are incorrect

A: treats 1 and 4 as zeroes. C: gives only one evaluated value. D: reverses the sign of the result.

Source: CBSE 2024 · Standard · Main · 30/4/1 · Q3
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 5 · Easy · 1 MARK

CBSE 2026 · Standard · Second examination · 30/7/1 · Q4

Find the zeroes of x² − x − 6.

A. 3, 2 B. −3, 2 C. 3, −2 D. −3, −2

Show Answer & Explanation

x² − x − 6 = (x − 3)(x + 2)

x − 3 = 0 or x + 2 = 0

Zeroes: 3 and −2

Correct answer: C — 3, −2

Common trap: The zeroes must have sum 1 and product −6.

Why the other choices are incorrect

A and D: give product +6. B: gives sum −1 instead of 1.

Source: CBSE 2026 · Standard · Second examination · 30/7/1 · Q4
Wording lightly normalised. Solutions prepared by Team TutorVertex.

Zeroes & coefficients

QUESTION 6 · Easy · 1 MARK

CBSE 2023 · Standard · Main · 30/4/1 · Q8

If α and β are the zeroes of x² − 1, find α + β.

A. 2 B. 1 C. −1 D. 0

Show Answer & Explanation

a = 1, b = 0

α + β = −b/a = 0

Correct answer: D — 0

Common trap: The constant term is −1; the coefficient of x is 0.

Why the other choices are incorrect

A: adds the magnitudes of the roots. B and C: give individual roots instead of their sum.

Source: CBSE 2023 · Standard · Main · 30/4/1 · Q8
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 7 · Easy · 1 MARK

CBSE 2023 · Standard · Main · 30/4/1 · Q17

If α and β are the zeroes of 4x² − 3x − 7, find 1/α + 1/β.

A. 7/3 B. −7/3 C. 3/7 D. −3/7

Show Answer & Explanation

α + β = 3/4; αβ = −7/4

1/α + 1/β = (α + β)/(αβ)

= (3/4) ÷ (−7/4) = −3/7

Correct answer: D — −3/7

Common trap: Divide the sum by the product, keeping the negative sign.

Why the other choices are incorrect

A and B: invert the required ratio. C: loses the negative sign of the product.

Source: CBSE 2023 · Standard · Main · 30/4/1 · Q17
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 8 · Moderate · 1 MARK

CBSE 2023 · Standard · Main · 30/2/1 · Q9

One zero of 6x² + 37x − (k − 2) is the reciprocal of the other. Find k.

A. −4 B. −6 C. 6 D. 4

Show Answer & Explanation

Reciprocal zeroes have product 1.

−(k − 2)/6 = 1

−k + 2 = 6

k = −4

Correct answer: A — −4

Common trap: The constant term is −(k − 2), not k − 2.

Why the other choices are incorrect

B: ignores the +2 after opening the brackets. C and D: lose or reverse the minus sign.

Source: CBSE 2023 · Standard · Main · 30/2/1 · Q9
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 9 · Easy · 1 MARK

CBSE 2023 · Standard · Main · 30/2/1 · Q16

If α and β are the zeroes of x² − ax − b, find α² + β².

A. a² − 2b B. a² + 2b C. b² − 2a D. b² + 2a

Show Answer & Explanation

α + β = a; αβ = −b

α² + β² = (α + β)² − 2αβ

= a² − 2(−b) = a² + 2b

Correct answer: B — a² + 2b

Common trap: The product is −b, so subtracting twice the product adds 2b.

Why the other choices are incorrect

A: uses b instead of −b for the product. C and D: interchange the roles of a and b.

Source: CBSE 2023 · Standard · Main · 30/2/1 · Q16
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 10 · Easy · 1 MARK

CBSE 2024 · Standard · Main · 30/2/1 · Q9

If α and β are the zeroes of 5x² + 3x − 7, find 1/α + 1/β.

A. −3/7 B. 3/5 C. 3/7 D. −5/7

Show Answer & Explanation

α + β = −3/5; αβ = −7/5

1/α + 1/β = (α + β)/(αβ)

= (−3/5) ÷ (−7/5) = 3/7

Correct answer: C — 3/7

Common trap: Both the sum and product are negative; their quotient is positive.

Why the other choices are incorrect

A: loses one negative sign. B: uses the leading coefficient as the denominator. D: does not use the sum/product ratio.

Source: CBSE 2024 · Standard · Main · 30/2/1 · Q9
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 11 · Moderate · 1 MARK

CBSE 2024 · Standard · Main · 30/5/1 · Q15

If α and β are the zeroes of kx² − 30x + 45k and α + β = αβ, find k.

A. −2/3 B. −3/2 C. 3/2 D. 2/3

Show Answer & Explanation

Since the polynomial is quadratic, k ≠ 0.

α + β = 30/k; αβ = 45k/k = 45

30/k = 45

k = 30/45 = 2/3

Correct answer: D — 2/3

Common trap: Cancel k in the product before solving.

Why the other choices are incorrect

A and B: introduce a negative sign. C: reverses 30/45.

Source: CBSE 2024 · Standard · Main · 30/5/1 · Q15
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 12 · Moderate · 1 MARK

CBSE 2025 · Standard · Main · 30/2/1 · Q16

If −4 is a zero of p(x) = x² − x − (2 + 2k), find k.

A. 3 B. 9 C. 6 D. −9

Show Answer & Explanation

p(−4) = 0

16 + 4 − 2 − 2k = 0

18 − 2k = 0

k = 9

Correct answer: B — 9

Common trap: Subtracting x at x = −4 gives +4.

Why the other choices are incorrect

A and C: do not satisfy p(−4) = 0. D: changes the sign when solving 2k = 18.

Source: CBSE 2025 · Standard · Main · 30/2/1 · Q16
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 13 · Moderate · 1 MARK

CBSE 2026 · Basic · Main · 430/5/1 · Q12

The sum of the zeroes of 3x² − kx + 6 is 2. Find k.

A. 2 B. −6 C. −2 D. 6

Show Answer & Explanation

a = 3; b = −k

Sum = −b/a = k/3

k/3 = 2

k = 6

Correct answer: D — 6

Common trap: The two negative signs in −b cancel.

Why the other choices are incorrect

A: gives the sum rather than k. B and C: keep an incorrect minus sign.

Source: CBSE 2026 · Basic · Main · 430/5/1 · Q12
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 14 · Moderate · 1 MARK

CBSE 2021–22 · Standard · Term 1 · held 4 December 2021 · 030/2/4 · Q30

If α and β are the zeroes of x² − (k + 6)x + 2(2k − 1) and α + β = (1/2)αβ, find k.

A. −7 B. 7 C. −3 D. 3

Show Answer & Explanation

α + β = k + 6

αβ = 2(2k − 1)

k + 6 = (1/2) × 2(2k − 1) = 2k − 1

k = 7

Correct answer: B — 7

Common trap: The factor 1/2 cancels the factor 2 in the product.

Why the other choices are incorrect

A: changes the sign of k = 7. C and D: do not satisfy k + 6 = 2k − 1.

Source: CBSE 2021–22 · Standard · Term 1 · held 4 December 2021 · 030/2/4 · Q30
Wording lightly normalised. Solutions prepared by Team TutorVertex.

Forming polynomials

QUESTION 15 · Easy · 1 MARK

CBSE 2023 · Basic · Main · 430/4/1 · Q1

A quadratic polynomial has sum of zeroes −3 and product 2. Which is suitable?

A. x² + 3x + 2 B. x² − 3x + 2 C. x² − 3x − 2 D. x² + 3x − 2

Show Answer & Explanation

A suitable polynomial is x² − (sum)x + product.

= x² − (−3)x + 2

= x² + 3x + 2

Correct answer: A — x² + 3x + 2

Common trap: The x coefficient is the negative of the sum.

Why the other choices are incorrect

B: gives sum +3. C: gives sum +3 and product −2. D: gives product −2.

Source: CBSE 2023 · Basic · Main · 430/4/1 · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 16 · Easy · 1 MARK

CBSE 2023 · Standard · Main · 30/5/1 · Q1

How many polynomials can have zeroes −3 and 5?

A. only one B. infinitely many C. exactly two D. at most two

Show Answer & Explanation

For every non-zero real k, k(x + 3)(x − 5) has zeroes −3 and 5.

There are infinitely many choices of k.

Correct answer: B — infinitely many

Common trap: The leading coefficient is not fixed.

Why the other choices are incorrect

A, C and D: place a finite limit on k, although any non-zero real multiplier works.

Source: CBSE 2023 · Standard · Main · 30/5/1 · Q1
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 17 · Easy · 1 MARK

CBSE 2023 · Basic · Supplementary · 430/C/1 · Q16

Which quadratic polynomial has zeroes 7 and 0?

A. x(x² − 7) B. 7x² − 1 C. (1/7)(x² − x) D. 7(x² − 7x)

Show Answer & Explanation

Zeroes 7 and 0 give factors (x − 7) and x.

7(x² − 7x) = 7x(x − 7)

The non-zero multiplier 7 does not change the zeroes.

Correct answer: D — 7(x² − 7x)

Common trap: Check both the degree and the zeroes.

Why the other choices are incorrect

A: is cubic. B: is not zero at x = 0. C: has zeroes 0 and 1.

Source: CBSE 2023 · Basic · Supplementary · 430/C/1 · Q16
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 18 · Moderate · 1 MARK

CBSE 2026 · Standard · Main · 30/5/1 · Q3

Which polynomial has zeroes −3 and 8?

A. x² + 5x − 4 B. (x + 3)(−x + 8) C. a(x² + 5x − 24), a ≠ 0 D. x² − 24

Show Answer & Explanation

A zero −3 gives the factor x + 3.

A zero 8 gives the factor x − 8.

(x + 3)(−x + 8) = −(x + 3)(x − 8)

Multiplying by −1 does not change the zeroes.

Correct answer: B — (x + 3)(−x + 8)

Common trap: A negative leading coefficient does not change the zeroes of a factored polynomial.

Why the other choices are incorrect

A: fails at both proposed zeroes. C: gives zeroes 3 and −8. D: gives zeroes ±√24, not −3 and 8.

Source: CBSE 2026 · Standard · Main · 30/5/1 · Q3
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 19 · Easy · 1 MARK

CBSE 2026 · Basic · Second examination · 430/7/1 · Q7

A quadratic polynomial has sum of zeroes 2 and product −7. Which is suitable?

A. x² − 2x + 7 B. 4(x² + 2x − 7) C. (x − 2)(x + 7) D. 3(x² − 2x − 7)

Show Answer & Explanation

A suitable polynomial is k[x² − (sum)x + product], k ≠ 0.

Use sum 2 and product −7.

3(x² − 2x − 7) has the required sum and product.

Correct answer: D — 3(x² − 2x − 7)

Common trap: A non-zero multiplier does not change the zeroes.

Why the other choices are incorrect

A: gives product +7. B: gives sum −2. C: gives sum −5 and product −14.

Source: CBSE 2026 · Basic · Second examination · 430/7/1 · Q7
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 20 · Easy · 1 MARK

CBSE 2021–22 · Standard · Term 1 · held 4 December 2021 · 030/2/4 · Q18

Which quadratic polynomial has product of zeroes 5 and sum of zeroes 8? (k ≠ 0)

A. k(x² − 8x + 5) B. k(x² + 8x + 5) C. k(x² − 5x + 8) D. k(x² + 5x + 8)

Show Answer & Explanation

A suitable quadratic is k[x² − (sum)x + product], k ≠ 0.

Use sum 8 and product 5.

Required polynomial: k(x² − 8x + 5).

Correct answer: A — k(x² − 8x + 5)

Common trap: Read product and sum in the order given; do not swap them.

Why the other choices are incorrect

B: gives sum −8. C: swaps the sum and product. D: gives sum −5 and product 8.

Source: CBSE 2021–22 · Standard · Term 1 · held 4 December 2021 · 030/2/4 · Q18
Wording lightly normalised. Solutions prepared by Team TutorVertex.

Graphs & number of zeroes

QUESTION 21 · Easy · 1 MARK

CBSE 2025 · Standard · Main · 30/4/1 · Q17

Which statement is always true for a polynomial p(x) of degree 3?

A. p(x) has at most two distinct zeroes. B. p(x) has at least two distinct zeroes. C. p(x) has exactly three distinct zeroes. D. p(x) has at most three distinct zeroes.

Show Answer & Explanation

A non-zero polynomial of degree n has at most n distinct real zeroes.

Here n = 3.

Therefore, p(x) has at most three distinct zeroes.

Correct answer: D — p(x) has at most three distinct zeroes.

Common trap: Degree gives a maximum number of distinct zeroes, not an exact count.

Why the other choices are incorrect

A: x³ − x has three distinct zeroes. B and C: x³ has only one distinct zero, 0.

Source: CBSE 2025 · Standard · Main · 30/4/1 · Q17
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 22 · Easy · 1 MARK

CBSE 2026 · Basic · Main · 430/4/1 · Q6

The graph of p(x) = k is a horizontal line above the x-axis. How many zeroes does p(x) have?

Graph redrawn from the cited paper.

A. 0 B. 1 C. 2 D. infinitely many

Show Answer & Explanation

Zeroes occur where the graph meets the x-axis.

This horizontal line never meets the x-axis.

Number of zeroes = 0.

Correct answer: A — 0

Common trap: The y-intercept is not a zero of the polynomial.

Why the other choices are incorrect

B and C: the line has no x-axis intersection. D: applies to p(x) = 0, whose graph lies on the x-axis.

Source: CBSE 2026 · Basic · Main · 430/4/1 · Q6
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 23 · Easy · 1 MARK

CBSE 2021–22 · Standard · Term 1 · held 4 December 2021 · 030/2/4 · Q2

A polynomial graph crosses the x-axis at 3 points and touches it at 2 other points. How many distinct zeroes does it have?

A. 1 B. 2 C. 3 D. 5

Show Answer & Explanation

Each distinct point on the x-axis represents one zero.

Crossings: 3; additional touching points: 2

Number of distinct zeroes = 3 + 2 = 5.

Correct answer: D — 5

Common trap: A point where the graph only touches the x-axis still represents a zero.

Why the other choices are incorrect

A and B: count only some touching points. C: counts crossings but misses the two touching points.

Source: CBSE 2021–22 · Standard · Term 1 · held 4 December 2021 · 030/2/4 · Q2
Wording lightly normalised. Solutions prepared by Team TutorVertex.

Official CBSE sample-paper MCQs

QUESTION 24 · Easy · 1 MARK · SAMPLE PAPER

CBSE Sample Paper · 2022–23 · Basic · Q3

If 2 is a zero of x² + 3x + k, find k.

A. 10 B. −10 C. 5 D. −5

Show Answer & Explanation

Substitute x = 2 and set the polynomial equal to 0.

4 + 6 + k = 0

k = −10

Correct answer: B — −10

Common trap: A zero makes the value of the polynomial 0.

Why the other choices are incorrect

A: misses the minus sign when moving 10. C and D: do not satisfy 4 + 6 + k = 0.

Source: CBSE Sample Paper · 2022–23 · Basic · Q3 · Official marking scheme
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 25 · Moderate · 1 MARK · SAMPLE PAPER

CBSE Sample Paper · 2022–23 · Standard · Q3

If α and β are the zeroes of px² − 2x + 3p and α + β = αβ, find p.

A. −2/3 B. 2/3 C. 1/3 D. −1/3

Show Answer & Explanation

Since the polynomial is quadratic, p ≠ 0.

α + β = 2/p; αβ = 3p/p = 3

2/p = 3

p = 2/3

Correct answer: B — 2/3

Common trap: The product simplifies to 3, not 3p.

Why the other choices are incorrect

A and D: give a negative sum instead of 3. C: gives a sum of 6 instead of 3.

Source: CBSE Sample Paper · 2022–23 · Standard · Q3 · Official marking scheme
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 26 · Easy · 1 MARK · SAMPLE PAPER

CBSE Sample Paper · 2025–26 · Basic · Q3

How many polynomials can have −2 and 5 as zeroes?

A. one B. two C. three D. infinitely many

Show Answer & Explanation

For any non-zero real k, k(x + 2)(x − 5) has zeroes −2 and 5.

Infinitely many different non-zero multipliers are possible.

Correct answer: D — infinitely many

Common trap: The zeroes do not determine a unique leading coefficient.

Why the other choices are incorrect

A, B and C: impose a finite count although the non-zero multiplier can take infinitely many values.

Source: CBSE Sample Paper · 2025–26 · Basic · Q3 · Official marking scheme
Wording lightly normalised. Solutions prepared by Team TutorVertex.

QUESTION 27 · Moderate · 1 MARK · SAMPLE PAPER

CBSE Sample Paper · 2025–26 · Standard · Q12

The zeroes of ax² + bx + c are equal, with a ≠ 0 and c ≠ 0. Which statement must be true?

A. c and b have opposite signs B. c and a have opposite signs C. c and b have the same signs D. c and a have the same signs

Show Answer & Explanation

Let the equal zeroes be r and r.

Their product is r² = c/a.

Since c ≠ 0, r ≠ 0 and r² > 0.

Thus c/a > 0, so c and a have the same signs.

Correct answer: D — c and a have the same signs

Common trap: Use the product of the equal zeroes; the sign of b can vary.

Why the other choices are incorrect

A and C: b can have either sign, depending on the sign of the repeated zero. B: would make c/a negative, but r² is positive.

Source: CBSE Sample Paper · 2025–26 · Standard · Q12 · Official marking scheme
Wording lightly normalised. Solutions prepared by Team TutorVertex.

Frequently asked questions

How do I find the sum and product of zeroes?

For ax² + bx + c, a ≠ 0, the sum is −b/a and the product is c/a.

How do I form a quadratic polynomial from its zeroes?

If the zeroes are α and β, use k(x − α)(x − β), where k is any non-zero real number.

How many zeroes does a graph show?

Count the distinct points where the graph meets the x-axis, including points where it touches the axis.

Are Assertion–Reason questions included?

This set contains standalone MCQs. Assertion–Reason questions are a separate resource type.

Is this every Polynomials question from 2022–2026?

No. This is a selected set of 27 questions with paper references; it does not claim complete coverage.

Continue practising

Polynomials chapter overview · Polynomials written-answer questions · Polynomials worksheets · Real Numbers MCQs

Question-paper sources

NCERT Polynomials chapter

Key rules for this chapter

A zero r satisfies p(r) = 0.
For ax² + bx + c, a ≠ 0: α + β = −b/a and αβ = c/a.
A quadratic with zeroes α and β is k(x − α)(x − β), k ≠ 0.
Count distinct x-axis intersections to find the number of real zeroes.
A non-zero polynomial of degree n has at most n distinct real zeroes.

How this question bank is prepared

Selected Polynomials MCQs from CBSE Basic and Standard board papers and official sample papers (2022–2026). Paper codes and question numbers are provided. The 2022 cycle includes 2021–22 Term 1, held in December 2021; its board-paper copy is hosted by Career Launcher. Wording is lightly normalised; worked solutions and difficulty labels are prepared by Team TutorVertex. Sample-paper questions are labelled by academic session and kept separate from board-exam questions. This is not a complete five-year collection.

CBSE Class 10 Polynomials MCQs(2022–2026)

Zeroes & polynomial values

Find the zeroes of x² + 4x + 3.

What is the degree of the zero polynomial?

Find the zeroes of 2x² − 3x − 9.

For p(x) = x² − 5x + 6, find p(1) + p(4).

Find the zeroes of x² − x − 6.

Zeroes & coefficients

If α and β are the zeroes of x² − 1, find α + β.

If α and β are the zeroes of 4x² − 3x − 7, find 1/α + 1/β.

One zero of 6x² + 37x − (k − 2) is the reciprocal of the other. Find k.

If α and β are the zeroes of x² − ax − b, find α² + β².

If α and β are the zeroes of 5x² + 3x − 7, find 1/α + 1/β.

If α and β are the zeroes of kx² − 30x + 45k and α + β = αβ, find k.

If −4 is a zero of p(x) = x² − x − (2 + 2k), find k.

The sum of the zeroes of 3x² − kx + 6 is 2. Find k.

If α and β are the zeroes of x² − (k + 6)x + 2(2k − 1) and α + β = (1/2)αβ, find k.

Forming polynomials

A quadratic polynomial has sum of zeroes −3 and product 2. Which is suitable?

How many polynomials can have zeroes −3 and 5?

Which quadratic polynomial has zeroes 7 and 0?

Which polynomial has zeroes −3 and 8?

A quadratic polynomial has sum of zeroes 2 and product −7. Which is suitable?

Which quadratic polynomial has product of zeroes 5 and sum of zeroes 8? (k ≠ 0)

Graphs & number of zeroes

Which statement is always true for a polynomial p(x) of degree 3?

The graph of p(x) = k is a horizontal line above the x-axis. How many zeroes does p(x) have?

A polynomial graph crosses the x-axis at 3 points and touches it at 2 other points. How many distinct zeroes does it have?

Official CBSE sample-paper MCQs

If 2 is a zero of x² + 3x + k, find k.

If α and β are the zeroes of px² − 2x + 3p and α + β = αβ, find p.

How many polynomials can have −2 and 5 as zeroes?

The zeroes of ax² + bx + c are equal, with a ≠ 0 and c ≠ 0. Which statement must be true?

Frequently asked questions

Continue practising

CBSE Class 10 Polynomials MCQs
(2022–2026)