LIWA

Polynomials

CBSE Class 10 · Maths · Chapter 2

Past board exam questions

CBSE 2027 sample paper · 1 mark

If α and β are the Zeroes of the polynomial 2x2 - 4x - 5, the value of (α - β)2 is

  1. 4
  2. 6
  3. 14
  4. 56
Show answer
14

CBSE 2027 sample paper · 1 mark

If f(x) = px2 + qx + r, p ≠ 0 and p + r = q, then one of the zeroes of f(x) is:

  1. (q)/(p)
  2. (r)/(p)
  3. -(r)/(p)
  4. -(q)/(p)
Show answer
-(r)/(p)

CBSE 2027 sample paper · 1 mark

Assertion (A): If zeroes of the polynomial (2k - 1)x2 + 4x - 3 are reciprocal of each other, then k = –1. Reason (R): If a = c, then zeroes of the polynomial ax2 + bx + c, a ≠ 0 are reciprocal of each other.

  1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
  3. Assertion (A) is true but Reason (R) is false.
  4. Assertion (A) is false but Reason (R) is true.
Show answer
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

CBSE 2027 sample paper · 2 marks

If one zero of the quadratic polynomial 2x2 - 3x + p is 3, find the value of p. Also, find the other zero.

Show answer
Since 3 is a zero of p(x) = 2x2 - 3x + p: 2(3)2 - 3(3) + p = 0 ⇒ 18 - 9 + p = 0 ⇒ p = -9. Let the other zero be β. Sum of zeroes: 3 + β = (-(-3))/(2) = (3)/(2) ⇒ β = -(3)/(2).

CBSE 2027 sample paper · 3 marks

If α and β are the zeroes of the quadratic polynomial 2x2 - 8x + 5, then find the value of (α + (1)/(β)) × (β + (1)/(α)).

Show answer
α + β = (8)/(2) = 4 and αβ = (5)/(2). (α + (1)/(β))(β + (1)/(α)) = (αβ + 1)/(β) × (αβ + 1)/(α) = ((αβ + 1)2)/(αβ) = (((5)/(2) + 1)2)/((5)/(2)) = (49/4)/(5/2) = (49)/(10).

CBSE 2026 board paper · 1 mark

If α and β are the roots of quadratic equation x2 - 7x + 11 = 0, then the value of (α2 + β2) is

  1. 27
  2. 29
  3. 31
  4. 33
Show answer
27

CBSE 2026 board paper · 1 mark

If the zeroes of the polynomial p(x) = 2x2 - 7x + 6 are α and β, then the value of (1)/(α) + (1)/(β) is

  1. (7)/(2)
  2. (6)/(7)
  3. (-7)/(6)
  4. (7)/(6)
Show answer
(7)/(6)

CBSE 2026 board paper · 1 mark

If m and n are the zeroes of the polynomial f(x) = 2x2 - 8 - 8x, then the value of m2 + n2 is :

  1. 0
  2. 32
  3. 24
  4. 16
Show answer
24