SOLUTION: Find all the solutions of {{{ x^3+3x^2+3x+2=0 }}} given that -2 is a root

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Question 153063: Find all the solutions of +x%5E3%2B3x%5E2%2B3x%2B2=0+ given that -2 is a root
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since -2 is a root then (x+2) is one factor of the equation.
You can divide the original polynomial by (x+2) to find the quadractic factor.
%28x%5E3%2B3x%5E2%2B3x%2B2%29%2F%28x%2B2%29=x%5E2%2Bx%2B1
Now find the roots of x%5E2%2Bx%2B1.
x%5E2%2Bx%2B1=0
Using the quadratic formula,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29+
x+=+%28-1+%2B-+sqrt%28+1-4+%29%29%2F%282%29+
x+=+%28-1+%2B-+sqrt%28+-3+%29%29%2F%282%29+
x+=+%28-1+%2B-+sqrt%28+3+%29i%29%2F%282%29+
The solutions are x=-2 and x+=+%28-1+%2B-+sqrt%28+3+%29i%29%2F%282%29+.