Find the values of $k$ for which the given equation has real and equal roots
$2 x^{2} - 10 x + k = 0$

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Solution

The given equation is $2 x^{2} - 10 x + k = 0$

Here, $a = 2, b = - 10, c = k$

$∴ D = b^{2} - 4 a c = {(- 10)}^{2} - 4 \times 2 \times k = 100 - 8 k$

The given equation will have real and equal roots, if
$D = 0 \Rightarrow 100 - 8 k = 0 \Rightarrow k = \frac{100}{8} = \frac{25}{2}$

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