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Math Help - [SOLVED] Proving?

  1. #1
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    [SOLVED] Proving?

    If (x - a)^2 is a factor of x^3 + mx^2 + n, prove that 27n + 4m^3 = 0
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  2. #2
    MHF Contributor red_dog's Avatar
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    Let f(x)=x^3+mx^2+n

    If (x-a)^2 is a factor of f, then f(a)=0, \ f'(a)=0

    f(a)=0\Rightarrow a^3+ma^2+n=0

    f'(a)=0\Rightarrow 3a^2+2am=0\Rightarrow a(3a+2m)=0

    If a\neq 0\Rightarrow a=-\frac{2m}{3}

    Now replace a in f(a)=0
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  3. #3
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    Lol Thanks. I nearly found it but my a was \frac{-2}{3}. Thanks for clearing it up for me.
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