Question

If the roots of $5x^2-kx+1=0$ are real and distinct, then
(a) $-2\sqrt{5}<k<2\sqrt{5}$
(b) $k>2\sqrt{5}$ only
(c) $k<-2\sqrt{5}$ only
(d) either $k>2\sqrt{5}$ or $k<-2\sqrt{5}$

Answer 1

(d) either $k>2\sqrt{5}$ or $k<-2\sqrt{5}$

$$\begin{gathered} \text{It is given that the roots of the equation (5}{x}^2-kx+1=0)\text{are real and distinct}\text{.} \\ \therefore (b^2-4ac)>0 \\ \Rightarrow {(-k)}^2-4\times 5\times 1>0 \\ \Rightarrow k^2-20>0 \\ \Rightarrow k^2>20 \\ \Rightarrow k>\sqrt{20}\text{or}k<-\sqrt{20} \\ \Rightarrow k>2\sqrt{5}\text{or}k<-2\sqrt{5} \end{gathered}$$