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June 20th, 2012, 07:47 AM  #1 
Senior Member Joined: Sep 2011 Posts: 395 Thanks: 0  Sum & Product of the Roots of a Quadratic Equation
Having a bit of trouble with this one. Can anyone help me out? Many thanks. Q. For what value of m are the roots of the equation equal but opposite in sign. Attempt: Sum of roots: => => => Product of roots: => => => => => => => => => => => ... Ans.: (From text book): m = 1 
June 20th, 2012, 07:59 AM  #2 
Member Joined: Jun 2012 From: UK Posts: 39 Thanks: 0  Re: Sum & Product of the Roots of a Quadratic Equation
You were virtually there, and then wandered off into deep doodoo. Just considering the sum of the roots gets you to (m+1)/3=0 and hence m=.... The only other thing you need to consider is that the product of the roots is nonzero (otherwise both roots are zero), and that's true, so you're done. 
June 20th, 2012, 08:12 AM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: Sum & Product of the Roots of a Quadratic Equation Hello, bilano99! You had the answer . . . You just zoomed past it. Quote:  
June 20th, 2012, 08:34 AM  #4 
Senior Member Joined: Sep 2011 Posts: 395 Thanks: 0  Re: Sum & Product of the Roots of a Quadratic Equation
D'oh!!! Thanks, guys.

June 20th, 2012, 09:32 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 18,241 Thanks: 1438 
If the roots are p and p, where p > 0, the equation is effectively 3(x + p)(x  p) = 0, i.e. 3x²  3p² = 0, so m = 1.


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