Quadratic Equations
What is a quadratic equation?
A quadratic equation is an equation that can be written in a form like this: ax^{2} + 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 ax^{2} = bx – c, but simply rearranging the equation doesn’t change the fact that it is a quadratic equation.
Standard Form
An equation of the form ax^{2} + 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 ax^{2} + bx +c = 0, a ≠ 0 If ak^{2} + bk +c = 0.
Note 1: if k is a root of ax^{2} + bx +c = 0, then we say that
 X=k satisfies the equation ax^{2} + bx +c = 0 or
 X=k is a solution of the equation ax^{2} + bx +c = 0.
Note 2: The roots of a Quadratic Equation ax^{2} + bx +c = 0 are called the zeros of the polynomial ax^{2} + bx +c .
Here are some examples:
2x^{2} + 5x + 3 = 0  In this one a=2, b=5 and c=3  
x^{2} − 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.