Let f(x)= x^4 + 25x^3 + 303x^2 + 1529x + 2030. Given that -8 + 9i is a root of f(x), list all of the roots including the complex roots.

Answer 1

The polynomial has real coefficients, so

-8 - 9i MUST be a solution

The factors are (x+8) - 9i and (x+8) + 9i

Multiplying these together gives: x^2 + 16x + 145

Dividing this polynomial into f(x) gives x^2 + 9x + 14

which has solutions x=-7 and x=-2

The solution set is {x=-7, x=-2, x = -8 +or- 9}