SOLUTION: The number x=-2i is a zero of polynomial P(x)=x^4+2x^3+x^2+8x-12. Find all four zeros of this polynomial. I have -3, -2, and 1

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The number x=-2i is a zero of polynomial P(x)=x^4+2x^3+x^2+8x-12. Find all four zeros of this polynomial. I have -3, -2, and 1      Log On


   

Question 762649: The number x=-2i is a zero of polynomial P(x)=x^4+2x^3+x^2+8x-12. Find all four zeros of this polynomial.
I have -3, -2, and 1
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Your found root of -2 is wrong.

You should find through Rational Roots Theorem and synthetic division, roots of -3, +1, and then you still would have a quadratic binomial of %28x%5E2%2B4%29. Solving the equation x%5E2%2B4=0 for x will give you -2i and %2B2i

Briefly, you should have made a process roughly equivalent to this:
Check for root -3;
Remainder 0, quotient x%5E3-x%5E2%2B4x-4
Check for root +1;
Remainder 0, quotient x%5E2%2B4
Solve the quadratic for its roots and find they are -2i and 2i.