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Cubic Function

  1. Feb 19, 2008 #1

    Aki

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    Hey I need help with this proof:

    Consider the cubic function: x^3 + bx^2 + cx + d = 0 . If the two solutions of the cubic function are not equal, ie r != s, but r=-s, then prove that bc=d.

    Thanks
     
  2. jcsd
  3. Feb 20, 2008 #2

    Gib Z

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    Homework Helper

    I'll give you help on this one, but please, next time post these problems in the Homework Help section. Its not just for our sake, you'll get a faster reply there too.

    -------------
    If all coefficients are real, by the complex conjugate root theorem you know that since two of the roots are real, s and -s, then the third root must be real as well. So now use the factor theorem and write the polynomial as a product of its factors,

    [tex]x^3+bx^2+cx+d = (x-k)(x^2-s^2)[/tex].

    Equate coefficients and see what you get.
     
  4. Feb 21, 2008 #3

    Aki

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    Very helpful. Thanks a lot Gib Z
     
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