Question

Find the values of $k$ for which the given equation has real roots
$5x^2-kx+1=0$

Answer 1

The given equation is $5x^2-kx+1=0$

Here, $a=5,b=-k,c=1$

$\therefore D=b^2-4ac={(-k)}^2-4\times 5\times 1=k^2-20$

The given equation will have real roots if
$D\ge 0$

$\Rightarrow k^2-20\ge 0\Rightarrow k\le -\sqrt{20}ork\ge \sqrt{20}[\because x^2-a^2\ge 0\Rightarrow x\le -aorx\ge a]$