Find the values of $k$ for which the given equation has real and equal roots
$2 x^{2} + 3 x + k = 0$

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Solution

The given equation is $2 x^{2} + 3 x + k = 0$

Here, $a = 2, b = 3, c = k$

$∴ D = b^{2} - 4 a c = 9 - 4 \times 2 \times k = 9 - 8 k$

The given equation will have real and equal roots, if

$D = 0 \Rightarrow 9 - 8 k = 0 \Rightarrow k = \frac{9}{8}$

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Find the value of $k$ for which the equation, ${2 x}^{2} + 3 x + k = 0$ distinct real roots.

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