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Math Help - algebra

  1. #1
    Senior Member
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    algebra

    Factorise f(x)=x^4-5x^3+11x^2-7x-24

    I found f(x)=(x+1)(x-3)(x^2-3x+6)

    Hence , solve the equation 24x^4+7x^3-11x^2+5x-1

    I can just see that the coefficient and the sign swapped .. but i am not sure what to do ?
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  2. #2
    MHF Contributor red_dog's Avatar
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    Let g(x)=24x^4+7x^3-11x^2+5x-1.

    f\left(\frac{1}{x}\right)=\frac{1}{x^4}-\frac{5}{x^3}+\frac{11}{x^2}-\frac{7}{x}-24=

    =-\frac{24x^4+7x^3-11x^2-5x+1}{x^4}=-\frac{g(x)}{x^4}

    Then, g(x)=0\Rightarrow f\left(\frac{1}{x}\right)=0.

    But f\left(\frac{1}{x}\right)=\left(\frac{1}{x}+1\righ  t)\left(\frac{1}{x}-3\right)\left(\frac{1}{x^2}-\frac{3}{x}+6\right)

    Can you continue?
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