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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- Jul 28th 2008, 08:20 PMlax600I 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 - Jul 28th 2008, 09:58 PMCaptainBlack
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