CBSE Class 10 Maths (Basic) 2025 · Paper 430(B)/S · Question 27(a)

Polynomials 3 marks Medium

Find the quadratic polynomial whose zeroes are

- 3

and

5

. Verify the relation between the coefficients and the zeroes of the polynomial.

Answer

p (x) = x^{2} - 2 x - 15

(or

k (x^{2} - 2 x - 15)

for any

k \neq = 0

). Here

a = 1

b = - 2

c = - 15

. Sum of zeroes

= - 3 + 5 = 2

and

- \frac{b}{a} = - \frac{- 2}{1} = 2

; product of zeroes

= (- 3) \times 5 = - 15

and

\frac{c}{a} = \frac{- 15}{1} = - 15

. Hence the relation is verified.

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