SOLUTION: Solve 2m^3 + 5m^2 - 13m-5=0, given -1/2 is a root

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Question 1193958: Solve 2m^3 + 5m^2 - 13m-5=0, given -1/2 is a root
Found 2 solutions by Theo, Solver92311:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
unfortunately m = -1/2 is not a root of the equation.
i replaced m with -1/2 in the equation and the result was 2.5.
i did the same using synthetic division and got the same result.
i graphed the equation as well and it shows that the roots are:
m = -3.977
m = -3.45
m = 1.822
unless i'm doing something terribly wrong, i don't see m = -1/2 as a root of this equation.

Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


is NOT a root of C.f. the following synthetic division: 

        ---------------------
-1/2    2    5    -13    -  5
            -1    - 2     7.5
        ---------------------
        2    4    -15     2.5


Since the remainder is non-zero, the divisor is not a root. is not a root either. 

        ---------------------
1/2     2    5    -13    -  5
             1      3    -  5
        ---------------------
        2    6    -10    - 10


In fact, no divisor of the form where is a factor of the constant term and is a factor of the lead coefficient results in a remainder of zero. Therefore your cubic equation has no rational roots.

The only way to solve this equation is to use the General Cubic Equation. I'm not that much of a glutton for punishment.

Just on the off chance that you made TWO typographical errors when stating your problem, it is true that has a rational root at .

John

My calculator said it, I believe it, that settles it

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