Question

Solve the given quadratic equation by using the formula method, $x^2-4x+2=0$

Answer 1

The given quadratic equation $x^2-4x+2=0$ is in the form $a{x}^2+bx+c=0$ where $a=1,b=-4$ and $c=2$.

We know that the quadratic formula is $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, therefore, substitute $a=1,b=-4$ and $c=2$ in $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ as follows:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-(-4)\pm \sqrt{(-4{)}^2-(4\times 1\times 2)}}{2\times 1}=\frac{4\pm \sqrt{16-8}}{2}$

$=\frac{4\pm \sqrt{8}}{2}=\frac{4\pm \sqrt{4\times 2}}{2}=\frac{4\pm 2\sqrt{2}}{2}=\frac{2(2\pm \sqrt{2})}{2}=2\pm \sqrt{2}$

Hence, $x=2+\sqrt{2}$ or $x=2-\sqrt{2}$.