If roots of the equation $2 x^{2} + 3 (k - 2) x + 4 - k = 15 x$ are negative of each other, then $k$ equals

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Solution

The correct option is D 7
Given quadratic equation
$2 x^{2} + 3 (k - 2) x + 4 - k = 15 x$
$\Rightarrow 2 x^{2} + 3 (k - 7) x + 4 - k = 0$
Let $α, - α$ be the roots
$α - α = 3 (k - 7)$
$\Rightarrow k = 7$

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