Question

Solve the equation

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

Answer 1

The given equation is $x^2-2x+4=0$

Compare the given quadratic with standard form $a{x}^2+bx+c=0$

Solve the quadratic equation using quadratic formula

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

$$\begin{gathered} \Rightarrow x=\frac{-(-2)\pm \sqrt{{(-2)}^2-4\times 1\times 4}}{2\times 1} \\ \Rightarrow x=\frac{2\pm \sqrt{4-16}}{2} \\ \Rightarrow x=\frac{2\pm \sqrt{-12}}{2} \\ \Rightarrow x=\frac{2\pm 2\sqrt{3}i}{2} \\ \Rightarrow x=1\pm \sqrt{3}i \end{gathered}$$

Hence, the solution of the given quadratic equation is $x=1\pm \sqrt{3}i$