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Discriminant

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Question

Find $k$ for which the sum & product of the roots of the roots of quadratic equation $k x^{2} - 4 x + 4 k = 0$ are equal.

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Solution

$k x^{2} - 4 x + 4 k = 0$
$\Rightarrow$ Sum of products $= \frac{4}{k}$
Product $= \frac{4 k}{k} = 4$
$\Rightarrow \frac{4}{k} = k$
$k^{2} = 4$
$k = \pm 2$
Hence, the answer is $\pm 2.$

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