SOLUTION: Write a polynomial equation with roots 2 and -6i. X^3 - _ x^2 + _ x - _ = 0 This is what I have so far. (x-2)(x+6i) (x^2 -2x +6i - 12i)

Algebra ->  Equations -> SOLUTION: Write a polynomial equation with roots 2 and -6i. X^3 - _ x^2 + _ x - _ = 0 This is what I have so far. (x-2)(x+6i) (x^2 -2x +6i - 12i)      Log On


   

Question 852485: Write a polynomial equation with roots 2 and -6i.
X^3 - _ x^2 + _ x - _ = 0
This is what I have so far.
(x-2)(x+6i)
(x^2 -2x +6i - 12i)
Found 2 solutions by ewatrrr, LinnW:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

(x-2)(x+6i)+highlight_green%28x-6i%29 

 (x^2 -2x +6i - 12i) = (x^2 -2x - 6i)

 (x^2 -2x -6i)(x-6i)  to finish Up

 x^3 - 2x^2 - 6ix  - 6ix^2 +12ix - 36   

combine Like terms

x^3 -2(1+3i)x^2 +6ix - 36

Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
To be a polynomial we need real coefficients
so we want something like:
(x-2)(x+6i)(x-6i)
This expands to
(x-2)( x^2 - (6i)^2 )
(x-2)( x^2 - ( 36i^2 ) )
(x-2)( x^2 - ( 36(-1)) )
(x-2)( x^2 + 36 ) expanded gives us
x^3 -2x^2 +36x -72
So our polynomial could be
x^3 -2x^2 +36x -72 = 0