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

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Question 1160750: If -2 is a root of z^3-8z^2+9z+58 = 0, then find the other two roots
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
To check that root with synthetic division:

Quadratic z%5E2-10z%2B29

Those roots are, using general solution for quadratic 'equation',
5%2B-+2i

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

z%5E3-8z%5E2%2B9z%2B58+=+0
to check if -2is a root, you can use synthetic division

z%5E3-8z%5E2%2B9z%2B58+=+0+divide by %28z+%2B+2%29


.......... (z%5E2+-+10z+%2B+29
%28z+%2B+2%29|z%5E3-8z%5E2%2B9z%2B58
......................z%5E3%2B2z........subtract
.........................-10z%5E2....bring down 9z
.........................-10z%5E2%2B9z
.........................-10z%5E2-20z........subtract
....................................+29z....bring down 58
....................................+29z%2B58
....................................+29z%2B58........subtract
..................................................+0....reminder is 0, so -2 is a root


use quotient z%5E2+-+10z+%2B+29 to find other two zeros using quadratic formula

z=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
z=%28-%28-10%29%2B-sqrt%28%28-10%29%5E2-4%2A1%2A29%29%29%2F%282%2A1%29
z=%2810%2B-sqrt%28100-116%29%29%2F2
z=%2810%2B-sqrt%28-16%29%29%2F2
z=%2810%2B-4i%29%2F2
z=%285%2B-2i%29
roots are:
z=5%2B2i
z=5-2i