SOLUTION: Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. Degree​ 5; ​ zeros: 9, i, 5 i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. Degree​ 5; ​ zeros: 9, i, 5 i      Log On


   

Question 1162417: Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.
Degree​ 5; ​ zeros: 9, i, 5 i
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-9%29%28x-i%29%28x%2Bi%29%28x-%285i%29%29%28x%2B5i%29
Simplify that.

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


If the coefficients are real, nonreal roots occur in conjugate pairs.

Since i is a root, -i is a root.
Since 5i is a root, -5i is a root.

That makes the required 5 roots: 9, i, -i, 5i, and -5i.