What do solutions to quadratic equations mean?

1 Answer

Answer:

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# .