Question

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

Answer 1

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

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