SOLUTION: find a third degree polynomial that has zeros: -2, -4i

Question 751407: find a third degree polynomial that has zeros: -2, -4i
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
x = -2 or x = -4i or x = 4i

x + 2 = 0 or x + 4i = 0 or x - 4i = 0

(x + 2)(x + 4i)(x - 4i) = 0

(x + 2)(x^2 - (4i)^2) = 0

(x + 2)(x^2 - 16i^2) = 0

(x + 2)(x^2 - 16(-1)) = 0

(x + 2)(x^2 + 16) = 0

x(x^2 + 16) + 2(x^2 + 16) = 0

x^3 + 16x + 2x^2 + 32 = 0

x^3 + 2x^2 + 16x + 32 = 0

Final Answer: y = x^3 + 2x^2 + 16x + 32
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