# If the equation

Question:

If the equation $x^{2}+5 k x+16=0$ has no real roots, then

(a) $k>\frac{8}{5}$

(b) $k<\frac{-8}{5}$

(c) $\frac{-8}{5}\frac{8}{5}$

(d) none of these

Solution:

(c) $\frac{-8}{5}\frac{8}{5}$

It is given that the equation $\left(x^{2}+5 k x+16=0\right)$ has no real roots.

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

$\Rightarrow(5 k)^{2}-4 \times 1 \times 16<0$

$\Rightarrow 25 k^{2}-64<0$

$\Rightarrow k^{2}<\frac{64}{25}$

\$\Rightarrow \frac{-8}{5}