CBSE Class 10 Maths (Standard) 2025 · Paper 30/6/1 · Question 32(b)

Quadratic Equations 5 marks Medium

Find the smallest value of

p

for which the quadratic equation

x^{2} - 2 (p + 1) x + p^{2} = 0

has real roots. Hence, find the roots of the equation so obtained.

Answer

The smallest value of

p

- \frac{1}{2}

; the equation then becomes

4 x^{2} - 4 x + 1 = 0

, whose roots are

\frac{1}{2}

and

\frac{1}{2}

(two equal roots).

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