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.
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
x^2 -2x + 3
so divide by that
x^2 -2x+3 | x^4-4x^3+4x^2-9
x^2 - 2x - 3 is a factor
(x-3)(x+1) are factors
so x = 3, x = -1 x = -1+isqrt2 , x=-1-isqrt2