SOLUTION: givn one zero, find all other zeros that can be either real or complex. p(x)=x^4-x^3+7x^2-9x-18 (3i is a zero)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: givn one zero, find all other zeros that can be either real or complex. p(x)=x^4-x^3+7x^2-9x-18 (3i is a zero)      Log On


   

Question 236848: givn one zero, find all other zeros that can be either real or complex.
p(x)=x^4-x^3+7x^2-9x-18 (3i is a zero)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: Recall that all complex zeros come in conjugate pairs. So -3i is also a zero. Now if x=3i, then x%5E2=-9 and x%5E2%2B9=0. Now just perform polynomial long division to simplify %28x%5E4-x%5E3%2B7x%5E2-9x-18%29%2F%28x%5E2%2B9%29. This will basically factor x%5E4-x%5E3%2B7x%5E2-9x-18 into two quadratics, which are easily solved by the quadratic formula.