SOLUTION: Find the polynomial function with integer coefficients that has-2+i and 4i as two of its zeros. f(x)=

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the polynomial function with integer coefficients that has-2+i and 4i as two of its zeros. f(x)=       Log On


   

Question 1127302: Find the polynomial function with integer coefficients that has-2+i and 4i as two of its zeros.
f(x)=

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The other two zeros are the conjugates or -2-i and -4i
The roots are
x-4i and x-(-4i) or x+4i. Multiplied together, that is x^2+16
x-(-2+i), which is x+2-i. And x+2+i
That product is
x^2+2x+ix+2x+4+2i-ix-2i+1 (minus i^2)
x^2+4x+5
The product of that and x^2+16 is
x^4+16x^2+4x^3+64x+5x^2+80
x^4+4x^3+21x^2+64x+80 ANSWER