Question

Find the values of x given X² - 4x + 13 = 0

Answer 1

The roots of qudratic equation are:

$x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a},$

where a = 1;

b = -4;

c = 13.

So,

$x_{1,2}=\frac{-(-4)\pm \sqrt{(-4)^2-4\cdot 1\cdot13}}{2\cdot 1}=2\pm 3\sqrt{-1}=2\pm 3i.$

Answer: x₁ = 2 + 3i, x₂ = 2 - 3i.