Value of $k$ for which the quadratic polynomial $k x^{2} + x + k$ has equal zeros.

\pm \frac{1}{2}

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\pm \frac{1}{3}

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\pm \frac{1}{4}

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\pm 1

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Solution

The correct option is D $\pm \frac{1}{2}$
For the equation $k x^{2} + x + k = 0$ to have equal zeros the discriminant must be zero.
Hence, $1 - 4 k^{2} = 0$

$=> k^{2} = \frac{1}{4}$

$∴ k = \pm \frac{1}{2}$

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