Find using the quadratic formula, the roots of the following quadratic equations, if they exist

x² + 4x + 5 = 0

Comparing x² + 4x + 5 = 0 with ax² + bx + c = 0 we get,

a = 1, b = 4, c = 5.

We know that,

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

Substituting values we get,

$\Rightarrow x = \dfrac{-4 \pm \sqrt{4^2 - 4(1)(5)}}{2(1)} \\[1em] = \dfrac{-4 \pm \sqrt{16 - 20}}{2} \\[1em] = \dfrac{-4 \pm \sqrt{-4}}{2}$

Since, b² - 4ac < 0

∴ roots are imaginary.

Hence, roots does not exist.