Determine the value of $k$ for which the $x = - a$ is a solution of the equation $x^{2} - 2 (a + b) x + 3 k = 0$

k = - \frac{a}{3} (3 a - 2 b)

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k = - \frac{a}{3} (3 a + b)

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k = - 2 \frac{a}{3} (a + 2 b)

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k = - \frac{a}{3} (3 a + 2 b)

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Solution

The correct option is A $k = - \frac{a}{3} (3 a + 2 b)$
Substituting x=a satisfies the equation

$\Rightarrow a^{2} + 2 a^{2} + 2 a b + 3 k = 0$

$\Rightarrow k = - \frac{a (3 a + 2 b)}{3}$

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