Solving Quadratic Equations Solving Quadratic Equations Using the Zero Product Using the Zero Product

PropertyProperty

Can you solve the puzzle Can you solve the puzzle below?below?

I’m thinking of two numbers.I’m thinking of two numbers.Their product is zero.Their product is zero.

Tell me one of the numbers.Tell me one of the numbers.

Can you solve the puzzle Can you solve the puzzle below?below?

I’m thinking of two numbers.I’m thinking of two numbers.Their product is zero.Their product is zero.

Tell me one of the numbers.Tell me one of the numbers.

Write, in your own words, why one of Write, in your own words, why one of the numbers has to be zero.the numbers has to be zero.

Now, let’s think of this algebraically.Now, let’s think of this algebraically.

AB=0AB=0

Tell me the value of one of the Tell me the value of one of the variables.variables.

Does it matter which one of the Does it matter which one of the variables is zero?variables is zero?

Could both of the variables be zero?Could both of the variables be zero?

Complete the following:Complete the following:

Example 1Example 1If (x-2) (x+3) = 0, then _____ = 0 or If (x-2) (x+3) = 0, then _____ = 0 or _____ = 0._____ = 0.

Example 2Example 2If x (x-1) = 0, then _____ = 0 or _____ If x (x-1) = 0, then _____ = 0 or _____ = 0.= 0.

Now let’s apply this to solving Now let’s apply this to solving some equations.some equations.

Example 3Example 3(x-4) (x+2) = 0(x-4) (x+2) = 0 The expressions have a zero The expressions have a zero

product.product.

x-4=0 x-4=0 oror x+2=0 x+2=0 Therefore, one of the numbers Therefore, one of the numbers must must be zero.be zero.

x=4 x=4 oror x= x=--2 2 Since we do not know which Since we do not know which one is one is equal to zero, we set them equal to zero, we set them both equal both equal to zero and we solve to zero and we solve each expression each expression for ‘x’.for ‘x’.

Now try a few of these on Now try a few of these on your own.your own.

SolveSolve1. (x-4)(x-5)=01. (x-4)(x-5)=0

2. x(2x+2)(3x-1)=02. x(2x+2)(3x-1)=0

3. 2x(x+2)=03. 2x(x+2)=0

Check your answers.Check your answers.

1. (x-4)(x-5)=01. (x-4)(x-5)=0 x=4 or x=4 or x=5x=5

2. x(2x+2)(3x-1)=02. x(2x+2)(3x-1)=0 x=0 or x=0 or x=-1 x=-1 or x=1/3 or x=1/3

3. 2x(x+2)=03. 2x(x+2)=0 x=0 or x=0 or x=-2x=-2