Question 982868: Find the polynomial with leading coefficient -2 that has degree 3 and roots 2 and 3i.
Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
I 'll do one exactly like it for you to use as a model to dop yours:
Find the polynomial with leading coefficient -3 that has degree 3 and roots 4 and 5i.
Since 5i is a root, so is -5i:
x = 4, x = 5i, x = -5i
x-4 = 0, x-5i = 0, x+5i = 0
p(x) = -3(x-4)(x-5i)(x+5i)
p(x) = -3(x-4)(x2+5ix-5ix-25i2
p(x) = -3(x-4)(x2-25(-1))
p(x) = -3(x-4)(x2+25)
p(x) = -3(x3-4x2+25x-100)
p(x) = -3x3+12x2-75x+300
Edwin
Answer by AnlytcPhil(1806)  (Show Source):
You can put this solution on YOUR website!
I 'll do one exactly like it for you to use as a model to dop yours:
Find the polynomial with leading coefficient -3 that has degree 3 and roots 4 and 5i.
Since 5i is a root, so is -5i:
x = 4, x = 5i, x = -5i
x-4 = 0, x-5i = 0, x+5i = 0
p(x) = -3(x-4)(x-5i)(x+5i)
p(x) = -3(x-4)(x2+5ix-5ix-25i2
p(x) = -3(x-4)(x2-25(-1))
p(x) = -3(x-4)(x2+25)
p(x) = -3(x3-4x2+25x-100)
p(x) = -3x3+12x2-75x+300
Edwin
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