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March 26, 2017

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Find all rational zeros of the function. Then (if necessary) use the depressed equation to find all roots of the equation f(x)=0
f(x)= 5x^4-11x^3-33x^2+77x-14

  • math - ,

    trying x = ±1, ±2, ± 7, ±1/5, ±2/5, ±7/5
    I found f(2) = 0
    and f(x) = (x-2)(5x^3 - x^2 - 35x + 7) = (x-2)g(x)
    x = ±7 didn't work in the first, so it certainly will not work in this one
    so try x = 1/5 in the cubic factor
    g(1/5) = 5(1/125) - 1/25 - 35(1/5) + 7 = 0

    so we have
    f(x) = (x-2)(5x-1)(x^2 - 7) after a division

    roots are
    x = 2, 1/5, ± √7

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