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CBSE Class 10 Maths (Basic) 2025 · Paper 430/4/1 · Question 32(a)

Quadratic Equations 5 marks Hard

It is given that

p^{2} x^{2} + (p^{2} - q^{2}) x - q^{2} = 0

;

(p \neq = 0)

.

(i)Show that the discriminant ( $D$ ) of above equation is a perfect square.
(ii)Find the roots of the equation.

Answer

(i)

D = (p^{2} - q^{2})^{2} + 4 p^{2} q^{2} = (p^{2} + q^{2})^{2}

, which is a perfect square. (ii) The roots are

x = \frac{q ^{2}}{p ^{2}}

and

x = - 1

.

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