Question

If the equation $x^2+5kx+16=0$ has no real roots, then
(a) $k>\frac{8}{5}$
(b) $k<\frac{-8}{5}$
(c) $\frac{-8}{5}<k>\frac{8}{5}$
(d) none of these

Answer 1

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

$$\begin{gathered} \text{It is given that the equation (}{x}^2+5kx+16=0)\text{has no real roots.} \\ \therefore (b^2-4ac)<0 \\ \Rightarrow {\left(5k\right)}^2-4\times 1\times 16<0 \\ \Rightarrow 25k^2-64<0 \\ \Rightarrow k^2<\frac{64}{25} \\ \Rightarrow \frac{-8}{5}<k<\frac{8}{5} \end{gathered}$$