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Math Help - Cubic Equation

  1. #1
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    Cubic Equation

    Show that x = 2 is on root of the equation x^e -4x^2 + (q + 4)x - 2q = 0.
    If the other two roots of this equation differ by 4, find the value of q, and solve the equation completely.

    Can someone show me how to do this q please? Thanks!
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Detanon View Post
    Show that x = 2 is on root of the equation x^e -4x^2 + (q + 4)x - 2q = 0.
    If the other two roots of this equation differ by 4, find the value of q, and solve the equation completely.

    Can someone show me how to do this q please? Thanks!
    HI

    do u mean x^3 instead of x^e for the leading term ? Because if its x^e , you will end up with 2^e-2^3\neq 0 .

    Assuming that its x^3-4x^2+(q+4)x-2q=0

    (x-2)(x^2-2x+q)=0

    Let a and b be the 2 other roots .

    a+b=2

    ab=q

    a-b=4

    So now there are enough information for you to solve for q .
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