If the equation
Question:

If the equation $9 x^{2}+6 k x+4=0$ has equal roots then $k=?$

(a) 2 or 0
(b) −2 or 0
(c) 2 or −2
(d) 0 only

Solution:

(c) 2 or −2

It is given that the roots of the equation $\left(9 x^{2}+6 k x+4=0\right)$ are equal.

$\therefore\left(b^{2}-4 a c\right)=0$

$\Rightarrow(6 k)^{2}-4 \times 9 \times 4=0$

$\Rightarrow 36 k^{2}=144$

$\Rightarrow k^{2}=4$

$\Rightarrow k=\pm 2$