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June 20th, 2012, 06:47 AM   #1
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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
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June 20th, 2012, 06:59 AM   #2
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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 non-zero (otherwise both roots are zero), and that's true, so you're done.
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June 20th, 2012, 07:12 AM   #3
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Re: Sum & Product of the Roots of a Quadratic Equation

Hello, bilano99!

You had the answer . . . You just zoomed past it.


Quote:









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June 20th, 2012, 07:34 AM   #4
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Re: Sum & Product of the Roots of a Quadratic Equation

D'oh!!! Thanks, guys.
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June 20th, 2012, 08:32 PM   #5
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If the roots are p and -p, where p > 0, the equation is effectively 3(x + p)(x - p) = 0, i.e. 3x - 3p = 0, so m = 1.
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