SOLUTION: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; Zeros:5, multiplicity 2;2i

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Question 668761: Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 4; Zeros:5, multiplicity 2;2i
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
if -5 + 2i is a root of the polynomial f(x)
and f(x) has real coefficients then the conjugate must also be a root .
thus -5 - 2i is also a root.
it is also said that 2 is a root of multiplicity 2.

(x + 5 + 2i) (x + 5 - 2i) (x - 2)^2
= ((x + 5)^2 + 4) (x^2 - 4x + 4)
= (x^2 + 10x + 29) (x^2 - 4x + 4)
= x^4 + 6x^3 - 7x^2 - 76x + 116