SOLUTION: find all of the roots for the equation: {{{x^4-x^3-5x^2-x-6}}}

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Question 4241: find all of the roots for the equation:
x%5E4-x%5E3-5x%5E2-x-6
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
Let f%28x%29+=+x%5E4-x%5E3-5x%5E2-x-6+
Use synthetic division
Try -1,+1 (fail) [factors of -6]
1 -1 -5 -1 -6 (-2
-2 +6 -2 +6
----------------
1 -3 +1 -3 0
So, x+2 is a factor of f(x) and we have f%28x%29=%28x%2B2%29%2A%28x%5E3-3x%5E2%2Bx-3%29
Clearly, %28x%5E3-3x%5E2%2Bx-3%29+=+%28x-3%29%28x%5E2%2B1%29
Hence, f%28x%29+=+%28x%2B2%29%2A%28x-3%29%2A%28x%5E2%2B1%29
The four roots are -2, 3 ,i and -i
Kenny