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October 14th, 2011, 10:32 PM   #1
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Value of two variables

If is a factor of . Find the values of p and q.

How to do this question?
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October 14th, 2011, 10:58 PM   #2
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Re: Value of two variables

Let



Note that are the two roots of

Put in the above equation.





So

Or, and

So and

-----------------------------------------------
Verification:
Put in the above equation:









So we get the same values of p and q.
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October 15th, 2011, 03:07 AM   #3
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Re: Value of two variables



Where
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October 16th, 2011, 11:32 AM   #4
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Code:
       x - 2x +  p-1
             ------------------------------------
x + 2x + 5  x^4       +     px     +  q
      x^4 + 2x +     5x
      -------------------
        - 2x + (p-5)x
        - 2x -     4x -  10x
        -------------------------
            (p-1)x +  10x +    q
            (p-1)x + 2(p-1)x + 5p-5
            ------------------------
Hence p = 6 and q = 25.

Alternatively, notice that the second factor must be x - 2x + 5 to make the product an even function,
then expanding (x + 2x + 5)(x - 2x + 5) gives x^4 + 6x + 25, so p = 6 and q = 25.
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