SOLUTION: Use the given zero to find the remaining zeros of the polynomial function P(x) =x^3+9x^2+x +9; -i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use the given zero to find the remaining zeros of the polynomial function P(x) =x^3+9x^2+x +9; -i      Log On


   

Question 1201672: Use the given zero to find the remaining zeros of the polynomial function
P(x) =x^3+9x^2+x +9; -i
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B%28i%29%29%28x-%28i%29%29
x%5E2-i%5E2
x%5E2-%28-1%29
x%5E2%2B1----------Try polynomial division with this as divisor to P(x), and see what more you can do after this.

Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
.

For this given polynomial, it is easy to find its zeros even without the given info about the root x= -i.


Apply grouping and factor


    x^3 + 9x^2 + x + 9 = (x^3 + 9x^2) + (x + 9) = x^2*(x+9) + (x+9) = (x+9)*(x^2+1).


Other zeroes are -9 and i.    ANSWER