Find the value of 'a' for which the quadratic equation $x^{2} - 2 a x + 2 a - 1 = 0$ has equal roots.

-1

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Solution

The correct option is B
1

$x^{2} - 2 a x + 2 a - 1 = 0$ has equal roots
$\Rightarrow D i s c r i m i n a n t = 0$
$\Rightarrow B^{2} - 4 A c = 0$
$\Rightarrow (- 2 a)^{2} - 4 (2 a - 1) = 0$
$\Rightarrow 4 a^{2} - 4 (2 a - 1) = 0$
$\Rightarrow 4 (a^{2} - (2 a - 1) = 0)$
$\Rightarrow a^{2} - 2 a + 1 = 0$
$\Rightarrow (a - 1)^{2} = 0$
$\Rightarrow a = 1$

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