polynomial grrr (1 Viewer)

[babygoose!]

hey i really suck at polys...can anyone help me out with this question..?

If P(x) = x^4 - 2x^3 - x^2 + 6x - 6 has a zero 1 - i , find the zeros of P(x) over C, and factorise P(x) fully over R..

THanx so much..!

 

[Affinity]

since it's a poly over the ring of real numbers, the complex zeroes must come in conjugate pairs..
that will give you 2 of the factors which allows you to factor the quartic into 2 linear polynomials and 1 quadratic, which you can then further factorize

ie 1+i is also a zero
so you can factorize into

[x-(1+i)][x-(1-i)][[ax^2 + bx + c] for some a,b,c

 

[babygoose!]

yeh thanx..i worked it out just after i posted it..thanx anyway