Sign DiagramsDate: 05/20/2002 at 03:43:17 From: Jessie Subject: Sign Diagrams (without graphing) There is a diagram in my text book that looks something like this: x2 - 1/2x | | + | _ | + __________________________________ | | -1/2 | I have no idea what it's telling me. Can you help me make sense of it? Date: 05/20/2002 at 12:24:14 From: Doctor Peterson Subject: Re: Sign Diagrams (without graphing) Hi, Jessie. When you have a polynomial factored, you can find the sign of the product by considering the sign of each factor separately. So let's first factor our expression as x^2 - 1/2 x = x(x - 1/2) The first factor, x, will of course be positive when x > 0 and negative when x < 0: --------------0+++++++++++++ x <-------------+------------> 0 The second factor, x - 1/2, will be positive when x > 1/2: -------------------0++++++++ x - 1/2 <-------------+----+-------> 0 1/2 Each factor has divided the number line into two parts, in different ways. If we put these together, we make a total of three regions of the number line, and can see what the product of the signs will be in each region: --------------0+++++++++++++ x -------------------0++++++++ x - 1/2 ++++++++++++++0----0++++++++ x(x - 1/2) <-------------+----+-------> 0 1/2 Whenever both factors are positive or both are negative, the product will be positive; when one is positive and the other negative, the product will be negative. That gives us a simple way to find the sign of the expression everywhere. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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