Algebra HW Help

Question

Write a polynomial f(x) that satisfies the given conditions.

Degree 3 polynomial with integer coefficients with zeros -9i and 9/7.

Find f(x)

Answer 1

imaginary zeros come in conjugate pairs. if -9i is a zero, so is +9i

then x=9i

and x^2= -9

X^2+9=0 = (x-9i)(x+9i)=0

(x^2+9) is a factor. The other factor is (x-9/7)

multiply them together

(x-9/7)(x^2+9) = (1/7)(7x-9)(x^2+9)

= (1/7)(x^3-9x^2 +63x -81)