Question

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

Answer 1

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

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

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

$=\frac{2\pm \sqrt{-12}}{2}$

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

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

$=\frac{2(1\pm 3i)}{2}=(1\pm 3i)$

Hence, $x=1+3i$ or $x=1-3i$.