Question

Find the roots of the following quadratic equation by quadratic formula.
$\frac{1}{2}{x}^2-\sqrt{11}x+1=0$

Answer 1

Given,

$\frac{1}{2}{x}^2-\sqrt{11}x+1=0$

$x^2-2\sqrt{11}x+2=0$

$a=1,b=2\sqrt{11},c=2$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-(-2\sqrt{11})\pm \sqrt{{(-2\sqrt{11})}^2-4\cdot 1\cdot 2}}{2\cdot 1}$

$=\frac{2\sqrt{11}\pm 6}{2}$

$x=\sqrt{11}\pm 3$