Onmatu- Pre-Calculus Article
Tweet 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.
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.