Solving Quadratic Equations
Quadratic Equation in One Variable: ax^{2} + bx + c = 0, where a, b and c are real numbers with a
≠ 0. We will solve these equations by several methods.
I. Solving Quadratic Equations by Factoring
The Zero Product Property: ab = 0 if and only if either a = 0 or b = 0 or both a and b equal zero.
II. Graphical Solution
Once the equation is written in the form ax^{2} + bx + c = 0, we can graph the left side
as y_{1} and find the x
intercepts. These xintercepts or zeros of the function are the solutions to the quadratic equation ax^{2}
+ bx + c = 0.
III. Square Root Property
The solution set of x^{2} = k is:
IV. Using the Quadratic Formula to Solve Quadratic Equations
If ax^{2} + bx + c = 0, a ≠ 0, then:
b^{2}  4ac is called the discriminant of the quadratic equation.
DISCRIMINANT AND ROOTS
If the discriminant is: 
Then the equation has: 
Positive 
Two real solutions 
Zero 
One real solution 
Negative 
No real solutions 
