Posted by **Brandon** on Wednesday, May 25, 2011 at 5:40pm.

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 -
**Damon**, Wednesday, May 25, 2011 at 6:40pm
(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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