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Discriminant

For what valu...

Question

For what value of $k$ are the roots of the quadratic equation $k x^{2} + 1 = - 4 x$ equal and real?

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Solution

Given the quadratic equation $k x^{2} + 1 = - 4 x$ .
or, $k x^{2} + 4 x + 1 = 0$ .
Now if the roots of the given equation be real and equal then we'll have,
$4^{2} - 4 k = 0$ [ Discriminant equal to $0$ ]
or, $k = 4$ .

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