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October 14th, 2011, 09:32 PM  #1 
Member Joined: Oct 2011 Posts: 81 Thanks: 0  Value of two variables
If is a factor of . Find the values of p and q. How to do this question? 
October 14th, 2011, 09:58 PM  #2 
Senior Member Joined: Aug 2008 Posts: 113 Thanks: 0  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. 
October 15th, 2011, 02:07 AM  #3 
Senior Member Joined: Jul 2011 Posts: 405 Thanks: 16  Re: Value of two variables Where 
October 16th, 2011, 10:32 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,034 Thanks: 2271  Code: x²  2x + p1  x² + 2x + 5 x^4 + px² + q x^4 + 2x³ + 5x²   2x³ + (p5)x²  2x³  4x²  10x  (p1)x² + 10x + q (p1)x² + 2(p1)x + 5p5  Alternatively, notice that the second factor must be x²  2x + 5 to make the product an even function, then expanding (x² + 2x + 5)(x²  2x + 5) gives x^4 + 6x² + 25, so p = 6 and q = 25. 

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