Question

Find the roots
$4x^2+4\sqrt{3x}+3=0$

Answer 1

Given: $4x^2+4\sqrt{3}x+3=0$

$4x^2+2\sqrt{3}x+2\sqrt{3}x+3=0$

$2x(2x+\sqrt{3})+\sqrt{3}(2x+\sqrt{3})=0$

$(2x+\sqrt{3})(2x+\sqrt{3})=0$

$x=-\frac{\sqrt{3}}{2},-\frac{\sqrt{3}}{2}$

Hence roots are same.