Find the values of k for each of the following quadratic equations, so that they have two equal roots.
$(i) 2 x^{2} + k x + 3 = 0$

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Solution

$(i) 2 x^{2} + k x + 3 = 0$
Comparing equation with $a x^{2} + b x + c = 0$ , we get
$a = 2, b = k a n d c = 3$
$D i s c r i m i n a n t = b^{2} - 4 a c$
$= (k)^{2} - 4 (2) (3)$
$= k^{2} - 24$
For equal roots,
Discriminant = 0
$k^{2} - 24 = 0$
$k^{2} = 24$
$k = \pm \sqrt{24} = \pm 2 \sqrt{6}$

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