Question

For what values of k, will quadratic equation ${9x}^2+3kx+4=0$ have real and equal roots?

• A. $\pm 4$
• B. $\pm 3$
• C. $\pm 2$
• D. $\pm 1$

Answer 1

The correct option is A $\pm 4$

Given equation is: ${9x}^2+3kx+4=0$
Comparing with ${ax}^2+bx+c=0$, we get
$\Rightarrow a=9,b=3k,c=4$
$D=b^2-4ac={\left(3k\right)}^2-4\left(9\right)\left(4\right)=9k^2-144$
Since the quadratic equation has real and equal roots.
$\Rightarrow D=0$
$\Rightarrow {9k}^2-144=0$
$\Rightarrow k^2=\frac{144}{9}=16$
$\Rightarrow k=\pm \sqrt{16}=\pm 4$
$\Rightarrow k=4$ and $-4$