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algebra 2

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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 - ,

    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 - ,

    my bad the original equation is:
    2X^4 - 9X^3 + 13X^2 - X - 5 = 0

  • algebra 2 - ,

    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 - ,

    oh I get it thanks

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