Form a a polynomial with real coefficients having the given degree & zeros?

Question

Degree 4: zeros; 3-2i ; 4, multiplicty 2
So far I have zeros as x-4 ; 3-2i ; 3+2i
Stuck there.. Help!!

Answer 1

You are correct up to that point.
The phrase "multiplicity 2" refers to the 4. It means that 4 is a double root, or 4 is a root "twice".
To get the polynomial we simply have to multiply out:
(x - (3 + 2i))(x - (3 - 2i))(x - 4)(x - 4)
Multiply the first two factors first. Bear in mind that i^2 = -1.
You should get:
x^2 - 6x + 13
Then multiply that by (x - 4).
You should get:
x^3 - 10x^2 - 11x - 52
Finally multiply that by (x - 4) again to get the final answer:
x^4 - 14x^3 + 29x^2 - 8x + 208