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Algebra 2

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Solve x^4-4x^3+4x^2-9=0 given that 1+i sqrt2 is a root.

I need all of the steps.
I need this ASAP because this assignment is due tomorrow.
Thanks

  • Algebra 2 - ,

    (x - 1 + i sqrt 2)(x -1 - i sqrt 2)
    is a factor
    multiply using distributive property
    x (x -1 - i sqrt2) = x^2 - x - ix sqrt2
    -1(x -1 - i sqrt 2)= -x +1 +isqrt2
    isqrt2(x -1 - i sqrt 2) = ixsqrt2 -isqrt2 +2
    which is
    x^2 -2x + 3
    so divide by that
    ********** __________________
    x^2 -2x+3 | x^4-4x^3+4x^2-9

    and get
    x^2 - 2x - 3 is a factor
    (x-3)(x+1) are factors
    so x = 3, x = -1 x = -1+isqrt2 , x=-1-isqrt2

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