Question

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

8
Degree 3 polynomial with integer coefficients with zeros -5i and
5

Answer 1

f(x) = x^3 -5x^2 +25x -125

Explanation:

For zero x=a, one of the factors is (x -a). If the polynomial has integer coefficients, its complex roots come in conjugate pairs. So, the roots are ...

roots: -5i, 5i, 5

factors: (x -(-5i))(x -5i)(x -5)

Multiplying these out gives your polynomial as ...

f(x) = (x^2 +25)(x -5)

f(x) = x^3 -5x^2 +25x -125