1. Solving Quadratic Equations Using the Quadratic Formula
Annette Williams MTSU

2. ax2 + bx + c = 0, with a not equal to 0.
We have already looked at the following methods for solving quadratic equations:
Graphing to find the zeros.
Factoring.
Using the Principle of Square Roots.
Now we will see that using the Quadratic Formula is a fourth and very important method. Unlike factoring and the Square Root Principle, it can be used for any quadratic of the form
ax2 + bx + c = 0, with a not equal to 0.

3. For an equation of the form ax2 + bx + c = 0, where a does not equal 0,
To use this formula an equation must be in the correct form, that is it must be set equal to 0. a, b, and c are the coefficients of the x2-term, the x-term, and the constant, respectively. They must not be mixed up, and they must all be on the same side of the equation. The equation below must be put in the correct form:
In this equation, after setting equal to 0, we find that a = 5, b = 3 and c = 8.

4. Solve.
Set equal to 0.
a = 3
b = 6
c = – 4
Fill in the formula.
Follow the proper order of operations.
Simplify the radical and the fraction if factorable.
Set Notation:

5. Solve x2 – 4x = 0
a = 5
b = –4
c = 0
Notice: – b = –(– 4) = 4
This could have been worked by the Factoring Method.
5x2 – 4x = 0
x(5x – 4) = 0
x = 0 or 5x – 4 = 0
x = 4/5

6. The discriminant is defined to be
This is the radicand from the quadratic formula. By calculating it you can know how many and what type of solutions the equation has. When the discriminant is positive there are two real solutions. If it is 0 there is only one real solution. If it is negative there are no real solutions.

7. Zero One Real Solution Positive Two Real Solutions Negative
The Discriminant:
Zero
One Real Solution
Positive
Two Real Solutions
Negative
No Real Solutions

8. Find the discriminant and tell from it how many and what type
of solutions each equation has.
No real
2 real
1 real
2 real