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 your own. Solve 1. (x-4)(x-5)=0 2. x(2 x+2)(3 x-1)=0 3. 2 x(x+2)=0

Check your answers. 1. (x-4)(x-5)=0 x=4 or x=5 2. x(2 x+2)(3 x-1)=0 x=0 or x=-1 or x=1/3 3. 2 x(x+2)=0 x=0 or x=-2

Solving quadratic equations X 2 + 7 x + 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

Set your equation to zero X 2 + 8 x = 65 X 2 + 8 x - 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

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