Definition of Quadratic Equation
A quadratic equation is an equation that can be written in a form like this: ax2 + bx +c = 0. In this equation, a, b, and c are constant numbers. The numbers a and b are called coefficients because they are multiplied with x. X is a variable. The equation can be written in different ways, such as ax2 = -bx – c, but simply rearranging the equation doesn’t change the fact that it is a quadratic equation.
An equation of the form ax2 + bx +c = 0,
- where a,b,c are real numbers
- and a ≠ 0
is called a quadratic equation in x.
Quadratic Equation Example:
Root of a Quadratic Equation: A real number k is called a root of the Quadratic Equation ax2 + bx +c = 0, a ≠ 0 If ak2 + bk +c = 0.
Note 1: if k is a root of ax2 + bx +c = 0, then we say that
- X=k satisfies the equation ax2 + bx +c = 0 or
- X=k is a solution of the equation ax2 + bx +c = 0.
Note 2: The roots of a Quadratic Equation ax2 + bx +c = 0 are called the zeros of the polynomial ax2 + bx +c .
Here are some examples:
|2x2 + 5x + 3 = 0||In this one a=2, b=5 and c=3|
|x2 − 3x = 0||This one is a little more tricky:
How do I solve a quadratic equation?
you can solve for x if you know the values of a, b and c.
When you solve a quadratic equation with the quadratic formula, you will always find two solutions. That is because there are always two values of x that satisfy the conditions of the quadratic formula. So you will never find exactly one solution. However, not all solutions are real numbers. When you calculate your solution to your quadratic equation, you might find that you have:
- two real number solutions,
- or, two solutions, both of which are complex numbers.