Find the values of $k$ for the following quadratic equation,so that it has two equal roots:
$2 x^{2}+k x+3=0$

(D) We know that if a quadratic equation $a x^{2}+b x+c=0$ has two equal roots,its discriminant $D = (b^{2}-4 a c)$ must be equal to $0$.
Given equation: $2 x^{2}+k x+3=0$
Comparing this with the standard form $a x^{2}+b x+c=0$,we get:
$a=2, b=k, c=3$
The discriminant is given by:
$D = b^{2}-4 a c$
$D = (k)^{2}-4(2)(3)$
$D = k^{2}-24$
For the equation to have two equal roots,we set the discriminant to $0$:
$k^{2}-24 = 0$
$k^{2} = 24$
$k = \pm \sqrt{24}$
$k = \pm 2 \sqrt{6}$