SOLUTION: Find the polynomial with leading coefficient -2 that has degree 3 and roots 2 and 3i.

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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(20059)   (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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