SOLUTION: If -2 is a root of {{{ z^3 - 8z^2 + 9z + 58 = 0 }}}, then find the other two roots.

Question 1181679: If -2 is a root of , then find the other two roots.
Answer by ikleyn(52760) (Show Source): You can put this solution on YOUR website!
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In fact,  -2  IS  a root of the given polynomial, and you can check it in one line, 
substituting the value of -2 into the polynomial

     -  +  + 58 = -8 - 32 - 18 + 58 = 0.



Therefore, the given polynomial is divisible by (z-2) without a remainer (according to the Remainder theorem)

and you can divide it using standard long division procedure 


     = z^2 - 10z + 29.


Find the roots of the last quadratic polynomial using the Quadratic Formula


     =  =  =  = 5 +- 2i.


ANSWER.  Two other roots of the given equation are  (5+2i)  and  (5-2i).

Solved.

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