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Math Help - I need a faster way of doing this

  1. #1
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    I need a faster way of doing this

    finding actual roots. Right now I'm using the Rational Root Theorem to list all the possible roots for this polynomial equation. Though it is to slow. I was wondering if anyone knew a faster way of doing this:

    26.) 10x^3-49x^2+68x-20=0
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by lax600 View Post
    finding actual roots. Right now I'm using the Rational Root Theorem to list all the possible roots for this polynomial equation. Though it is to slow. I was wondering if anyone knew a faster way of doing this:

    26.) 10x^3-49x^2+68x-20=0
    Sketch it, also Descartes rule of signs tells you that 1 or 3 roots are positive and none are negative.

    At x=0, 10x^3-49x^2+68x-20=-20, and at x=1, 10x^3-49x^2+68x-20=9.

    So there is a root between x=0 and x=1.

    This narrows the candidates for the first root down to 1/2, 1/5, 2/5 and 4/5.

    RonL
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