SOLUTION: Given the root 5+2i find all roots of the equation x^3-7x^2-x+87=0 This is my first time on this site asking a question. This was not in my book nor did my instructor go over th

Algebra ->  Equations -> SOLUTION: Given the root 5+2i find all roots of the equation x^3-7x^2-x+87=0 This is my first time on this site asking a question. This was not in my book nor did my instructor go over th      Log On


   

Question 722945: Given the root 5+2i find all roots of the equation x^3-7x^2-x+87=0
This is my first time on this site asking a question. This was not in my book nor did my instructor go over this. It was on a study guide and I have no clue. please help if you can.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
5+2i find all roots of the equation x^3-7x^2-x+87=0
You can use synthetic division

5+2i |1   -7     -1      87
     |     5+2i  -14+6i -87
      1   -2+2i  -15+6i   0

So we have factored the left side of the equation as:

[x-(5+2i)][x²+(-2+2i)x+(-15+6i)] = 0

Since 5+2i is a root, so is its conjugate 5-2i.  So
we use synthetic division again on

              x²+(-2+2i)x+(-15+6i) = 0

5-2i |1   -2+2i   -15+6i
     |     5-2i    15-6i
      1    3         0 

So the complete factorization is

[x-(5+2i)][x+(5+2i)](x+3) = 0

Set each equal to 0 and solve 

The three roots are 5+2i, 5-2i, and -3 

Edwin