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CBSE · Class 10 · Mathematics

Polynomials

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
The sum of the zeroes of the polynomial x2 − 8x + 7 is:
  1. 7
  2. −8
  3. 9
  4. 8
2.
The product of the zeroes of the polynomial 4x2 − 56x + 180 is:
  1. 180
  2. 14
  3. 45
  4. −45
3.
The zeroes of the polynomial x2 + 4x − 45 are:
  1. −9 and 5
  2. −5 and 9
  3. 5 and 9
  4. −9 and −5
4.
A quadratic polynomial whose zeroes have sum −3 and product 5 is:
  1. x2 + 3x + 5
  2. x2 − 3x − 5
  3. x2 − 3x + 5
  4. x2 − 5x − 3
5.
A quadratic polynomial can have at most:
  1. one zero
  2. two zeroes
  3. three zeroes
  4. infinitely many zeroes
6.
If −7 is a zero of the polynomial x2 + kx − 7, then k is:
  1. 6
  2. 1
  3. −6
  4. −7
7.
The sum of the zeroes of the cubic polynomial x3 − 8x2 + 11x + 20 is:
  1. −20
  2. −8
  3. 11
  4. 8
8.
Assertion (A): The sum of the zeroes of 3x2 − 27x + 60 is 10.
Reason (R): For ax2 + bx + c, the sum of the zeroes is −b/a.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
Find the zeroes of 6y2 − 25y + 25 and verify the relationship between the zeroes and the coefficients.
10.
Find a quadratic polynomial whose zeroes have sum 3/5 and product 1/5.
11.
Find the zeroes of t2 + 10t.
12.
Find the zeroes of 121y2 − 4.
13.
If α and β are the zeroes of x2 − 10x + 24, find the value of α2 + β2.
14.
If α and β are the zeroes of x2 − x − 30, find the value of 1/α + 1/β.
15.
For the cubic polynomial x3 − 5x2 − 9x + 45, find the sum of the zeroes, the sum of the products of the zeroes taken two at a time, and the product of the zeroes.
16.
One zero of 3x2 − 21x − 24 is 8. Find the other zero.
Section C — Word problems4 × 4 = 16 marks
17.
A toy rocket is launched straight up from the ground. Its height after t seconds is h(t) = −5t2 + 60t metres. Find the zeroes of h(t) and say what they mean.
18.
A shop's daily profit, in hundreds of rupees, from selling x dozen kites is P(x) = −x2 + 22x − 117. Find the zeroes of P(x). What do they tell the shopkeeper?
19.
A rectangular garden has a perimeter of 86 m and an area of 450 m2. Write a quadratic polynomial whose zeroes are its length and breadth, and find them.
20.
Without drawing it, find where the graph of y = x2 − 9x + 20 meets the x-axis and the y-axis.
AmbifulWorksheets
Practice that never repeats
CBSE · Class 10 · Mathematics

Answer key

Polynomials · AW-10M-POL-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) 8sum of zeroes = −b/a = 8
2(c) 45product of zeroes = c/a = 45
3(a) −9 and 5x2 + 4x − 45 = (x + 9)(x − 5)
4(a) x2 + 3x + 5x2 − (sum of zeroes)x + (product of zeroes) = x2 + 3x + 5
5(b) two zeroesthe degree is 2
6(a) 6(−7)2 + k × (−7) − 7 = 0, so k = 6
7(d) 8sum of zeroes = −b/a = 8
8(d) A is false, but R is true.A is false: −b/a = 9, not 10. R is true.
95/3 and 5/26y2 − 25y + 25 = (2y − 5)(3y − 5); sum = 25/6 = −b/a, product = 25/6 = c/a
105x2 − 3x + 1 (or any non-zero multiple of it)k[x2 − (3/5)x + (1/5)]; take k = 5 to clear the fractions
110 and −10t(t + 10) = 0, so t = 0 or t = −10
12−2/11 and 2/11(11y − 2)(11y + 2) = 0
1352α + β = 10, αβ = 24; α2 + β2 = (α + β)2 − 2αβ = 100 − 48 = 52
14−1/301/α + 1/β = (α + β)/αβ = 1 ÷ (−30) = −1/30
155; −9; −45−b/a = 5, c/a = −9, −d/a = −45
16−1sum of zeroes = −b/a = 7, so the other zero = 7 − 8 = −1
17t = 0 and t = 12: it leaves the ground at t = 0 and lands back after 12 seconds−5t(t − 12) = 0
18x = 9 and x = 13: there is no profit or loss at 9 or 13 dozen, and a profit in between−x2 + 22x − 117 = −(x − 9)(x − 13)
19x2 − 43x + 450; length 25 m, breadth 18 msum of zeroes = half the perimeter = 43, product = area = 450
20x-axis at (4, 0) and (5, 0); y-axis at (0, 20)y = 0 at the zeroes: (x − 4)(x − 5) = 0; at x = 0, y = 20