If the equation $x^{2} + k x + k = 0$ has only one solution, find the possible values of k.

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Solution

$x^{2} + k x + k = 0$ has only one solution.
$∴$ The discriminant $b^{2} - 4 a c = 0$
$∴ k^{2} - 4 k = 0$
$\Rightarrow k (k - 4) = 0$
$∴ k = 0$ or $k = 4$
So for $k = 0$ or $k = 4$ the equation $x^{2} + 4 x + 4 = 0$ has only one solution.

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