SOLUTION: Solve completely. x^4-3x^3-2x^2+10x-12=0

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Question 1134151: Solve completely. x^4-3x^3-2x^2+10x-12=0
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Several possible roots to test:
-12,-6,-4,-3,-2,-1,1,2,3,4,6,12;

The ones which will be found if you test using synthetic division should be -2 and +3.

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

x%5E4-3x%5E3-2x%5E2%2B10x-12=0+...write -3x%5E3 as -2x%5E3-x%5E3, +-2x%5E2 as 2x%5E2%2B2x%5E2-6x%5E2 and 10x as -2x%2B12x
x%5E4-2x%5E3%2B2x%5E2-x%5E3%2B2x%5E2-2x-6x%5E2%2B12x-12=0...group
%28x%5E4-2x%5E3%2B2x%5E2%29-%28x%5E3-2x%5E2%2B2x%29-%286x%5E2-12x%2B12%29=0..factor
x%5E2%28x%5E2-2x+%2B2+%29-x%28x%5E2-2x%2B2%29-6%28x%5E2-2x%2B2%29=0
%28x%5E2+-+x+-+6%29+%28x%5E2+-+2x+%2B+2%29+=+0
%28x%5E2%2B2x+-+3x+-+6%29+%28x%5E2+-+2x+%2B+2%29+=+0
%28%28x%5E2%2B2x%29+-%28+3x+%2B+6%29%29+%28x%5E2+-+2x+%2B+2%29+=+0
%28x%28x%2B2%29+-3%28+x+%2B+2%29%29+%28x%5E2+-+2x+%2B+2%29+=+0
%28x+-+3%29+%28x+%2B+2%29+%28x%5E2+-+2+x+%2B+2%29+=+0

=> two solutions are: highlight%28x++=+3%29 and highlight%28x++=+-2%29
next two solutions find using quadratic formula for
x%5E2+-+2+x+%2B+2+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29+
x+=+%282+%2B-+sqrt%28+4-8+%29%29%2F2+
x+=+%282+%2B-+sqrt%28+-4+%29%29%2F2+
x+=+%282+%2B-+2i%29%2F2+
x+=+%281+%2B-+i%29+
solutions: highlight%28x+=+1+%2B+i%29+ or highlight%28x+=+1+-+i%29+