### Solving Quadratic Equations Using the Zero Product Property

```Solving Quadratic Equations
Using the Zero Product Property
March 18, 2014
Can you solve the puzzle below?
I’m thinking of two numbers.
Their product is zero.
Tell me one of the numbers and
why you think it is that number.
Can you solve the puzzle below?
I’m thinking of two numbers.
Their product is zero.
Tell me one of the numbers.
Write, in your own words, why one of the
numbers has to be zero.
Now, let’s think of this algebraically.
AB=0
Tell me the value of one of the variables.
Zero Product Property
The product of two factors is zero only
when at least one of the factors is zero.
If ab = 0, then a=0 or b = 0
Does it matter which one of the variables is
zero?
Could both of the variables be zero?
Complete the following:
Example 1
If (x-2) (x+3) = 0, then _____ = 0 or
_____ = 0.
Example 2
If x (x-1) = 0, then _____ = 0 or _____ =
0.
Now let’s apply this to solving
some equations.
(x-4) (x+2) = 0
x-4=0 or x+2=0
x=4 or x=-2
The expressions have a zero product.
Therefore, one of the numbers must
be zero.
Since we do not know which one is
equal to zero, we set them both equal
to zero and we solve each expression
for ‘x’.
Now try a few of these on
Solve
1. (x-4)(x-5)=0
2. x(2x+2)(3x-1)=0
3. 2x(x+2)=0
1. (x-4)(x-5)=0
x=4 or x=5
2. x(2x+2)(3x-1)=0
x=0 or x=-1
or x=1/3
3. 2x(x+2)=0
x=0 or x=-2
X2 + 7x + 10 = 0
(x + 2)(x + 5) = 0
Factor
x + 2 = 0 or x + 5 = 0
X = -2
or x = -5
Set each to zero
Solve
X2 + 8x = 65
X2 + 8x - 65 = 0
Set to zero
(x + 13)(x – 5) = 0
Factor
X + 13 = 0
x = -13
Set to 0
Solve
or
x–5=0
or x = 5