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Solving Quadratic Equations Using the Zero Product Property

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Can you solve the puzzle below? Im thinking of two numbers. Their product is zero. Tell me one of the numbers.

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

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Now, lets think of this algebraically. AB=0 Tell me the value of one of the variables.

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Does it matter which one of the variables is zero? Could both of the variables be zero?

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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.

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Now lets apply this to solving some equations. Example 3 (x-4) (x+2) = 0 The expressions have a zero product. x-4=0 or x+2=0 Therefore, one of the numbers must be zero. x=4 or x=-2 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.

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Now try a few of these on your own. Solve 1. (x-4)(x-5)=0 2. x(2x+2)(3x-1)=0 3. 2x(x+2)=0

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Check your answers. 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

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