# Complex Roots of a Quadratic Equation

"How to solve the complex roots of a quadratic equation problems: the meaning of the discriminant, examples, and their solutions.

## Example 1

Previously, you've solved this example.

Quadratic formula

Let's solve the same equation

by using the quadratic formula

to find its complex roots.

√-79 = √79*i*

Imaginary numbers (*i*)

So, instead of just writing 'no real roots',

now you can write the roots in complex numbers.*x* = (1 ± √79*i*) / 8.

## Meaning of the Discriminant

Recall that the discriminant

determines the nature of the roots

of a quadratic equation.

If *D* < 0, it makes the radicand (-).

So there are no real roots.

This is what you've learned before.

But now you know how to solve (-) radicand:

√-1 = *i*.

Imaginary numbers (*i*)

So now you can say that

if *D* < 0,

then the quadratic equation has two imaginary roots.

## Example 2

*D* < 0.

So this quadratic equation has two imaginary roots.