Question

What do solutions to quadratic equations mean?

Answer 1

A complex number '`alpha`' is called a solution or root of a quadratic equation `f(x) = ax^2 + bx + c`
if `f(alpha) = aalpha^2 + balpha +c = 0`

Explanation:

If you have a function - `f(x) = ax^2 + bx + c`
and have a complex number - `alpha` .

If you substitute the value of `alpha` into `f(x)` 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(x) = x^2 - 8x + 15`

The roots of it will be 3 and 5 .

as `f(3) = 3^2 - 8*3 + 15 = 9 - 24 +15 = 0` and

`f(5) = 5^2 - 8*5 + 15 = 25 - 40 +15 = 0` .