Question:
If the roots of $5 x^{2}-k x+1=0$ are real and distinct, then
(a) $-2 \sqrt{5} (b) $k>2 \sqrt{5}$ only (c) $k<-2 \sqrt{5}$ only (d) either $k>2 \sqrt{5}$ or $k<-2 \sqrt{5}$
Solution:
(d) either $k>2 \sqrt{5}$ or $k<-2 \sqrt{5}$
It is given that the roots of the equation $\left(5 x^{2}-k x+1=0\right)$ are real and distinct.
$\therefore\left(b^{2}-4 a c\right)>0$
$\Rightarrow(-k)^{2}-4 \times 5 \times 1>0$
$\Rightarrow k^{2}-20>0$
$\Rightarrow k^{2}>20$
$\Rightarrow k>\sqrt{20}$ or $k<-\sqrt{20}$
$\Rightarrow k>2 \sqrt{5}$ or $k<-2 \sqrt{5}$