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Math Help - discriminant (fraction)

  1. #1
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    discriminant (fraction)

    Find the set of values of a for which the equation, \frac{2x^2-4ax+a^2+8}{(x-a)^2} has 2 distinct roots.

    While I know that this question can be solved by using b^2-4ac>0 using the equation 2x^2-4ax+a^2+8, I do not understand why (x-a)^2 can be ignored. Why is it that only the top of the fraction is considered?
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  2. #2
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    Re: discriminant (fraction)

    Quote Originally Posted by Punch View Post
    Find the set of values of a for which the equation, \frac{2x^2-4ax+a^2+8}{(x-a)^2} has 2 distinct roots.

    While I know that this question can be solved by using b^2-4ac>0 using the equation 2x^2-4ax+a^2+8, I do not understand why (x-a)^2 can be ignored. Why is it that only the top of the fraction is considered?
    because \frac{0}{any \, \, value \, \ne 0} = 0
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  3. #3
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    Re: discriminant (fraction)

    You may ignore the bottom only at your peril!!

    Before I thought I had a solution, I would want to know that x=a does NOT make the numerator vanish.
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  4. #4
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    Re: discriminant (fraction)

    However, your basic problem with finding "the set values of a for which the equation has 2 distinct roots" is that you don't has an equation!

    What did the problem really say?
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  5. #5
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    Re: discriminant (fraction)

    Quote Originally Posted by HallsofIvy View Post
    However, your basic problem with finding "the set values of a for which the equation has 2 distinct roots" is that you don't has an equation!

    What did the problem really say?
    The equation is as posted in post 1.
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