What is a 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 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:
What is the quadratic formula?
How do I solve a quadratic equation?
you can solve for x if you know the values of a, b and c.
- two real number solutions,
- or, two solutions, both of which are complex numbers.