If the roots of


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 $k<-2 \sqrt{5}$



(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 $k<-2 \sqrt{5}$


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