The value of k, of the roots of the equation $2 k x^{2} + 2 k x + 2 = 0$ are equal is

\frac{4}{5}

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Solution

The correct option is B $4$
If quadratic equation $a^{2} + b x + c = 0$ has equal roots
then $D = \sqrt{b^{2} - 4 a c} = 0$
In the given equation
$a = 2 k, b = 2 k, c = 2$
$D = \sqrt{(2 k)^{2} - 4.2 k .2} = 0$
$D = \sqrt{4 k^{2} - 16 k .} = 0$
$4 k^{2} - 16 k = 0$
$∴ k = 0, 4$
we ignore $k = 0$ , if k $=$ 0 then it wouldn't be quadratic
$∴ k = 4$

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