Algebra 2
posted by Brandon on .
Solve x^44x^3+4x^29=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

(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^44x^3+4x^29
and get
x^2  2x  3 is a factor
(x3)(x+1) are factors
so x = 3, x = 1 x = 1+isqrt2 , x=1isqrt2