Onmatu- Pre-Calculus Article

Quadratic equations


What is a quadratic equation? 

Quadratic means that a variable in the equation has highest degree equals two (2).
It is of the following form:

                   ax^2 + bx + c = 0.

Here we have a quadratic equation of a variable x. a, b and c are real numbers and we call them coefficients of the quadratic equation.
a is always different than zero, but coefficients b and c can be zeros (one of them or both at the same time) and the equation is still quadratic.
For example 
                             2x^2 = 0,
   
                          2x^2 - 3 = 0,

                             2x^2 = 8,

                             x^2 = -9,

are all quadratic equations.

Discriminant of a quadratic equation

We call D = b^2 - 4ac, a discriminant of a quadratic equation. The solutions of a quadratic equations depends on the sign of its discriminant. And this is how.
If D > 0, then the solutions are two different real numbers.
If D < 0, then the solutions are two different complex numbers.
If D = 0, then there is only one solution which is a real number.

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