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Math Help - Find all roots...

  1. #1
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    Jan 2009
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    Find all roots...

    Uhm, hi again you guys. ^^" I have root problems, it seems.
    And other problems. (I think I'm going to be posting up more problems because I have forgotten a lot of the stuff I've learned. This is like a review extra credit assignment.)

    Find all the roots of the equation f(x) = 6x^5-13x^4+27x^3+22x^2-78x+36=0
    It suggests using Rational Root Theorem, Descartes rule, and such. I only managed to find two roots...they are 1 and 2/3. I'm left with 6x^3-3x^2+18x+54=0 as the quotient...and when I try to continue trial and error with synthetic division, I can't find the other roots. Help please!
    Thank you.
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  2. #2
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    Quote Originally Posted by Jukixel View Post
    Uhm, hi again you guys. ^^" I have root problems, it seems.
    And other problems. (I think I'm going to be posting up more problems because I have forgotten a lot of the stuff I've learned. This is like a review extra credit assignment.)

    Find all the roots of the equation f(x) = 6x^5-13x^4+27x^3+22x^2-78x+36=0
    It suggests using Rational Root Theorem, Descartes rule, and such. I only managed to find two roots...they are 1 and 2/3. I'm left with 6x^3-3x^2+18x+54=0 as the quotient...and when I try to continue trial and error with synthetic division, I can't find the other roots. Help please!
    Thank you.
    By Descartes rule of signs there is exactly 1 negative root of this cubic, and a bit of trial and error (or the rational root theorem) suggests you try -3/2

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  3. #3
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    Joined
    Jan 2009
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    Oh, wow. xD Thanks a lot! When I did Descartes rule, I accidentally changed an even power's sign and ended up with 2 variations. ^^" That confused me and then I thought that there weren't any negative roots because it could vary by an even integer.
    Thank you!
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