Question

$x^2+5kx+16=0$ has no real roots, then :

• A. $k>\frac{8}{5}$
• B. $k>-\frac{8}{5}$
• C. $\frac{-8}{5}<k<\frac{8}{5}$
• D. $0<k<\frac{8}{5}$

Answer 1

The correct option is C $\frac{-8}{5}<k<\frac{8}{5}$

The discriminant of $x^2+5kx+16=0$ is

$D=\sqrt{25k^2-64}$

For no real roots $D<0$

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

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

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

$\Rightarrow |k|<\frac{8}{5}$

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

Option C is correct.