Find a polynomial function f with real coefficients that satisfies the given conditions. leading coefficient a= -1, degree n= 3, Zeros include -4 and -1i.

Question

Find a polynomial function f with real coefficients that satisfies the given conditions.

leading coefficient a= -1, degree n= 3, Zeros include -4 and -1i.

f(x) =  _____________

Leave your answer in partially factored form. Only multiply out the factors containing imaginary numbers!

Answer 1

f(x) = -(x+4)(x-i)(x+i)

= -(x+4)(x^2+1)

imaginary zeros come in conjugate pairs. if i is one zero, then -i is another zero.

take each zero, change its sign, then stick an x in front of it to give the corresponding factor