# Find the values k for which of roots of

Question:

Find the values $k$ for which of roots of $9 x^{2}+8 k x+16=0$ are real and equal

Solution:

Given:

$9 x^{2}+8 k x+16=0$

Here,

$a=9, b=8 k$ and $c=16$

It is given that the roots of the equation are real and equal; therefore, we have:

$D=0$

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

$\Rightarrow(8 k)^{2}-4 \times 9 \times 16=0$

$\Rightarrow 64 k^{2}-576=0$

$\Rightarrow 64 k^{2}=576$

$\Rightarrow k^{2}=9$

$\Rightarrow k=\pm 3$

$\therefore k=3$ or $\mathrm{k}=-3$