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Math Help - common roots(help please)

  1. #1
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    common roots(help please)

    a is a real number.If equations below have 2 roots in common what is the value of a?
    x^2-2x-5=0
    x^3-3x^2+a+1=0


    I found the answer but the question has two answers and I don't understand why :
    1)x1+x2=2
    x1+x2+x3=3 and x3=1.
    1-3+a+1=0 and a=1

    2) x1.x2.x3=-a-1
    x1.x2=-5
    and a=4

    Why did I find 2 answers?
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: common roots(help please)

    I don't understand the technique that you are attempting to use. The first equation has two roots - call them x1 and x2. You can deternine them using the quadratic equation. You can then solve for 'a' by setting the second equation equal to zero and rearranging to get:

    a = -x^3+3x^2+1

    You get a different value for 'a' when you replace x by either x1 or x2. There is no one value of 'a' that results in the second equation having the same two rots as the first.
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  3. #3
    MHF Contributor ebaines's Avatar
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    Re: common roots(help please)

    Sorry, this was a typo:

    Quote Originally Posted by ebaines View Post
    You can then solve for 'a' by setting the second equation equal to zero and rearranging to get:

    a = -x^3+3x^2+1
    It should be: a = -x^3+3x^2-1
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  4. #4
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    Re: common roots(help please)

    Many Thanks.
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