Zero Product PropertyDate: 02/14/98 at 12:42:56 From: Jessica Subject: Zero Product Property How do you find the answer to a zero product property question? If you could help it would be very helpful! Date: 02/17/98 at 21:48:48 From: Doctor Schwenoha Subject: Re: Zero Product Property The zero product property simply states that if the result of multiplying two or more numbers is zero, then one (or more) of the numbers must be zero. So, if AB = 0 then A = 0, B = 0, or both A and B are equal to zero. You could extend this to ABC = 0 and surmise that one of the three equals zero, or it could be that two of them equal zero or that all three equal zero. Take this thought to as many factors as you wish. Let's look at some typical algebra problems dealing with this property. x^2 - x = 0 factors to x(x-1) = 0 so we have two factors and either of them could equal zero. Set up both of them equal to zero to solve for the possibilities: x = 0 or x - 1 = 0 x = 1 We now have the solution that x = 0 or 1 to make our original equation true. Another problem might be x^2 - x - 6 = 0 this factors to (x + 2)(x - 3) = 0 and one of those factors must be zero, so either x + 2 = 0 or x - 3 = 0 and the solutions are x = -2 or x = 3 Now that you know the process for using the zero product property, what does it do for you? What do these possible values for x do for you? If you were graphing either of the equations in these examples, the solutions for x would tell you where the graph of the equation crosses the x-axis. In your algebra course of study I would guess that you are building to a place where you will need to use this information. -Doctor Schwenoha, The Math Forum Check out our Web site http://mathforum.org/dr.math/ |
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