SOLUTION: x^3-5x^2-11x+39. plz solv it

Question 964214: x^3-5x^2-11x+39. plz solv it

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
use descartes rule of signs to find the possible number of positive and negative real roots.
number of positive roots is 0 or 12.
number of negative roots is 1.
the possible real roots of a polynomial are factors of the constant term divided by factors of the leading coefficient.
here's a reference:
http://www.purplemath.com/modules/rtnlroot.htm
in your problem, possible roots are factors of 1 * 39 = 39
those factors are:
plus or minus 1,39
plus or minus 3,13
use synthetic division to find the roots.
since there has to be one negative root, i searched for the negative root first.
i started with -3 and got lucky.
x = -3 is one of the roots.
the factors become (x+3) * (x^2 - 8x + 13) = 0
i used the quadratic eqution to find the roots of x^2 - 8x + 13.
i got.
x = -3 (first root i found
x = (8 + sqrt(12)/2
x = (8 - sqrt(12)/2
those are your solutiions.
the references that will help you understand how to do synthetic division and how to find negative and positive roots are here:
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut37_syndiv.htm
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut38_zero1.htm

if you feel ambitious, you can also check out:
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut39_zero2.htm

here's a graph of your equation:

you have a root at x = -3, (8 - sqrt(12))/2), (8 + sqrt(12))/2

(8 - sqrt(12)/2 is about equal to 2.27.
(8 + sqrt(12)/2 is about equal to 5.73

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