CBSE Class 10 Maths (Standard) 2025 · Paper 30/4/1 · Question 30

Polynomials 3 marks Medium

α

and

β

are zeroes of a quadratic polynomial

p x^{2} + q x + 1

. Form a quadratic polynomial whose zeroes are

\frac{2}{α}

and

\frac{2}{β}

Answer

The required quadratic polynomial is

x^{2} + 2 q x + 4 p

; any non-zero constant multiple

k (x^{2} + 2 q x + 4 p)

has the same zeroes

\frac{2}{α}

and

\frac{2}{β}

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