Question:
Find the values of $k$ for which the quadratic equation $3 x^{2}+k x+3=0$ has real and equal roots?
Solution:
Let $3 x^{2}+k x+3=0$ be a quadratic equation.
It is given that, it has real and equal roots.
$\Rightarrow$ Discriminant $=0$
$\Rightarrow b^{2}-4 a c=0$
$\Rightarrow(k)^{2}-4(3)(3)=0$
$\Rightarrow k^{2}=36$
$\Rightarrow k=\pm 6$
Hence, the values of k are –6 and 6.