The value of $k$ , if 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 D $4$
$T h e g i v e n e q u a t i o n i s 2 k x^{2} + 2 k x + 2 = 0 \Rightarrow k x^{2} + k x + 1 = 0 I t i s o f t h e f o r m a x^{2} + b x + c = 0 ∴ a = b = k, c = 1. S i n c e t h e r o o t s a r e e q u a l w e h a v e b^{2} = 4 a c . S u b s t i t u t i n g t h e v a l u e o f a, b a n d c w e h a v e k^{2} = 4 k \Rightarrow k^{2} - 4 k = 0 \Rightarrow k (k - 4) = 0 ∴ e i t h e r k = 0 w h i c h i s i m p o s s i b l e i n t h i s c a s e a s i t i s c o e f f i c i e n t o f x^{2} i n t h e e q u a t i o n . ∴ W e r e j e c t k = 0 ∴ k - 4 = 0 \Rightarrow k = 4 (A n s)$

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