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}
(d) none of these
Solution:
(c) $\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}
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