SOLUTION: Find the integral root of . X^3-2X^2-X-6=0

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Question 936332: Find the integral root of
.
X^3-2X^2-X-6=0
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E3-2x%5E2-x-6=0
x%5E3-3x%5E2%2Bx%5E2-3x%2B2x-6=0...group
%28x%5E3-3x%5E2%29%2B%28x%5E2-3x%29%2B%282x-6%29=0..factor out
x%5E2%28x-3%29%2Bx%28x-3%29%2B2%28x-3%29=0
%28x-3%29%28x%5E2%2Bx%2B2%29+=+0
one solution is: if x-3=0 => x=3
use quadratic formula to find other two solutions:
x%5E2%2Bx%2B2+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29+
x+=+%28-1+%2B-+sqrt%28+1-8+%29%29%2F2+
x+=+%28-1+%2B-+sqrt%28+-7+%29%29%2F2+
x+=+%28-1+%2B-+sqrt%28+7+%29i%29%2F2+
so, we have complex solutions:
x+=+%28-1+%2B+sqrt%28+7+%29i%29%2F2+ or x+=+-1%2F2+%2B+sqrt%28+7+%29i%29%2F2+
and
x+=+%28-1+-+sqrt%28+7+%29i%29%2F2+ or x+=+-1%2F2-+sqrt%28+7+%29i%29%2F2+

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3-2x%5E2-x-6%29+