Posted by **Jessica** on Thursday, January 27, 2011 at 5:07pm.

2X^4-9X^3+3X^2-X-5=0

Given that one root is 2+i, solve the equation.

So far I have it set up like this:

2X^4-9X^3+3X^2-X-5/X^2-4X+5

I don't know how to get the answer, I know that I have to use long division but when I started to try it I kept getting weird answers. Please Help

- algebra 2 -
**Reiny**, Thursday, January 27, 2011 at 5:48pm
I think there is something wrong here,

either you have a typo in the opening equation, or the question is faulty.

If one root is 2+i, then 2-i must be another root

You correctly determined that

x^2 - 4x + 5 must then be a factor

When I divided that into the original, I got an answer of 2x^2 - x -11 with a remainder of -40x + 50

- algebra 2 -
**Jessica**, Thursday, January 27, 2011 at 5:55pm
my bad the original equation is:

2X^4 - 9X^3 + 13X^2 - X - 5 = 0

- algebra 2 -
**Reiny**, Thursday, January 27, 2011 at 6:02pm
Ok, this time my division was exact, as expected,

and I got 2x^2 - x - 1, which factors to

(2x + 1)(x - 1)

so the roots are

2+i, 2-i, -1/2, and 1

- algebra 2 -
**Jessica**, Thursday, January 27, 2011 at 6:12pm
oh I get it thanks

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