If the sum of the roots of the equation $5 x^{2} - 4 x + 2 + k (4 x^{2} - 2 x - 1) = 0$ is $6$ , then $k =$

- 1

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1

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\frac{13}{11}

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\frac{- 13}{11}

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Solution

The correct option is C $\frac{- 13}{11}$
Given sum of roots of
$(5 + 4 k) x^{2} - (4 + 2 k) x + 2 - k = 0$ is $6$
$\Rightarrow \frac{(4 + 2 k)}{(5 + 4 k)} = 6 ($ Since sum of roots is $- \frac{b}{a})$
$\Rightarrow 4 + 2 k = 30 + 24 k$
$22 k = - 26$
$k = \frac{- 13}{11}$

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