# What do solutions to quadratic equations mean?

A complex number '$\alpha$' is called a solution or root of a quadratic equation $f \left(x\right) = a {x}^{2} + b x + c$
if $f \left(\alpha\right) = a {\alpha}^{2} + b \alpha + c = 0$

#### Explanation:

If you have a function - $f \left(x\right) = a {x}^{2} + b x + c$
and have a complex number - $\alpha$ .

If you substitute the value of $\alpha$ into $f \left(x\right)$ and got the answer 'zero', then $\alpha$ is said to be the solution / root of the quadratic equation.

There are two roots for a quadratic equation .

Example :

Let a quadratic equation be - $f \left(x\right) = {x}^{2} - 8 x + 15$

The roots of it will be 3 and 5 .

as $f \left(3\right) = {3}^{2} - 8 \cdot 3 + 15 = 9 - 24 + 15 = 0$ and

$f \left(5\right) = {5}^{2} - 8 \cdot 5 + 15 = 25 - 40 + 15 = 0$ .