Question

Solve the following quadratic equation by using quadratic formula method: $x^2+4x+1=0$

Answer 1

The given quadratic equation is

$x^2+4x+1=0$

Here, $a=1,b=4,c=1$

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

$=\frac{-4\pm \sqrt{16-4\times 1\times 1}}{2}$

$=\frac{-4\pm 2\sqrt{3}}{2}$

$=\frac{-4+2\sqrt{3}}{2}$ or $\frac{-4-2\sqrt{3}}{2}$

$=\frac{-2(2-\sqrt{3})}{2}$ or $\frac{-2(2+\sqrt{3})}{2}$

$=-1(2-\sqrt{3})$ or $-1(2+\sqrt{3})$

$Roots=(-2+\sqrt{3},-2-\sqrt{3})$