1. Zero – product property
5-5 Quadratic equations
Zero – product property

2. Solving quadratic equations
Zero product property
After factoring a trinomial you can set each binomial equal to zero and solve for your variable
Example:
Solve x2 + 7x =18
First, put all terms on the left side of the equation and set the trinomial equal to zero
x2 + 7x – 18 = 0
Factor the trinomial into 2 binomials
(x + 9) (x-2) = 0
Set each binomial equal to zero and solve each part.
x + 9 = 0 x – 2 = 0
x = x = 2
The solutions are -9 and 2.

3. Solving by factoring square roots
Example: Solve 5x = 0
Rewrite the equation so the squared term is on the left side and the constant is on the right
5x2 = 180
Isolate the variable
Divide by 5 to isolate the x-squared term
x2 = 180/5
x2 = 36
Take the square root of each side to solve for x
x2 = 36
x =+ 6

4. Solving quadratic equations
Check the solutions back in the original problem. Sometimes one of the solutions won’t check. If the solution doesn’t check, it is thrown out.
x2 + 7x =18 x2 + 7x =18
x = -9 x = 2
(-9)2 + 7(-9) =18 (2)2 + 7(2) =18
81 – 63 = = 18
18 = = 18 (the answers check)

5. Try these two “different” problems:
2x2 + 4x =6
16x2 = 8x
2x2 + 4x – 6 = 0
2( x2 + 2x – 3)= 0 or 2x2 + 4x – 6 = 0
2(x+3) (x-1) = or (2x + 6) (x – 1) = 0
Divide by 2
(x + 3) (x – 1) = 0 or (2x + 6) (x – 1) = 0
x + 3 = 0; x-1 =0 or 2x+6 = 0 ; x-1 = 0
x = -3; x = 1 or 2x = -6 ; x = 1
x = -3 ; x = 1
The solutions are -3 and 1
Both methods yield the same answers
Check your answers in the original equation.
16x2 - 8x = 0
8x (2x – 1 ) = 0
8x = x – 1 = 0
x = x = 1
x = ½
The solutions are 0 and ½

6. Try these two “different” problems:
4x =0
3x2 – 24=0
4x2 = 25
Divide by 4
x2 = 25/4
x = + 5/2 Or
4x2 – 25 = 0 (rewrite the problem as the diff. of 2 squares)
(2x-5) (2x+5) = 0
2x-5 = 0 and 2x+5 = 0
x=5/ x = -5/2
The solutions are 5/2 and -5/2
Both methods yield the same answers
Check your answers in the original equation.
4x2 = 25
Divide by 4
x2 = 25/4
x = + 5/2 Or
4x2 – 25 = 0 (rewrite the problem as the diff. of 2 squares)
(2x-5) (2x+5) = 0
2x-5 = 0 and 2x+5 = 0
x=5/ x = -5/2
The solutions are 5/2 and -5/2
Both methods yield the same answers
Check your answers in the original equation.
3x2 = 24
Divide by 3
x2 = 8
x = + 8
The solutions are 8 and - 8

7. Homework
Chapter 5 packet ; 5-5 w/s
1, 5, 8, 9, 18, 28, 30