Polynomials II

Question

Given that f(x) is a cubic function with zeros at -4 and 2 i - 1 , find an equation for f(x) given that f(-6) = 1.

Answer 1

f(X)= a(x+4)[x-(-1+2i)][x-(-1-2i)]

 

multiply out the two expressions (after simplifying them) enclosed in square brackets; this gives you the irreducible quadratic factor, then multiply that by (x+4).   you now have the cubic, with a leading a factored out.

 

so use the given statement f(-6) = 1 to resolve what a is.

 

This will get you where you need to go.  The top line of my reply here uses the fact that complex roots occur in conjugate pairs.