How to solve a quadratic equation?

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A quadratic equation is an equation of the form

ax^2 + bx + c = 0 \ \ \ \ \ (1)

where

a,b,c \in \mathbb{R}\ and a \ne 0\ .

Let us assume that we are trying to solve this equation for real numbers only i.e. we are trying to find the real root(s) of the equation.

The value

D = b^2 - 4ac \ \ \ \ \ (*)

is called discriminant of the equation (1).

Case #1:

When D > 0, there are two distinct real solutions to (1) and they are:

x_{1,2} = {-b \pm \sqrt{b^2-4ac} \over 2a} \ \ \ \ \ (2)

Case #2:

When D = 0, there is one real solution to (1) which is:

x = -{b \over 2a} \ \ \ \ \ (3)

Case #3:

When D < 0, there are no real solutions to (1).

 

 

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