SOLUTION: given the polynomial p(x) = x^4-2x^3-7x^2+18-18 If one zero of P is 1-i, find the remaining zeros of P.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: given the polynomial p(x) = x^4-2x^3-7x^2+18-18 If one zero of P is 1-i, find the remaining zeros of P.      Log On


   

Question 1165191: given the polynomial p(x) = x^4-2x^3-7x^2+18-18
If one zero of P is 1-i, find the remaining zeros of P.
Answer by Seutip(231) About Me  (Show Source):
You can put this solution on YOUR website!
To find zeroes we should equate P(x) to 0
0+=+x%5E4-2x%5E3-7x%5E2%2B18x-18
Then factor out
0+=+%28x-3%29%28x%5E3%2Bx%5E2-4x%2B6%29 you can also factor out (x^3+x^2-4x+6) giving us
0+=+%28x-3%29%28x%2B3%29%28x%5E2-2x%2B2%29 I hope you know how to factor out easily,
but using foil method you will get 0+=+x%5E4-2x%5E3-7x%5E2%2B18x-18
When you multiply the factors with each other, there is nothing left to
factor out so our final equation now is:
0+=+%28x-3%29%28x%2B3%29%28x%5E2-2x%2B2%29
It will give us 3 sub-equations
x-3=0
x%2B3=0
and x%5E2%2B2x%2B2=0
x-3=0
One root is x=3
x%2B3=0
The other root is x=-3
and x%5E2%2B2x%2B2=0 using quadratic formula gives you
x=%28-1%2Bi%29x=%28-1-i%29
Hope that helps!!!!
Thank you and God bless!