SOLUTION: Find the zeros of the polynomial function by using the rational zeros theorem and synthetic division: F(x)= x^3-6x^2+13x-20

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Question 1192188: Find the zeros of the polynomial function by using the rational zeros theorem and synthetic division:
F(x)= x^3-6x^2+13x-20
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You can do this on your own. The roots to check for are plus and minus of 1, 2, 4, 5. Just find one of them, and then either factoring or general solution for quadratic equation can give the other two.

The only rational zero is 4, and then the other two are either irrational, or complex.

----- 


+4   |    1    -6    13    -20
     |
     |          4   -8      20
     |___________________________
          1    -2    5       0       see this remainder is 0, meaning that +4 is one of the zeros.

Those coefficients now of DEGREE 2 being for x%5E2-2x%2B5.

General Solution for Quadratic Equation for x%5E2-2x%2B5=0 gives
x=%282%2B-+sqrt%28%28-2%29%5E2-4%2A1%2A5%29%29%2F2
x=%282%2B-+sqrt%284-20%29%29%2F2
x=%282%2B-+sqrt%28-16%29%29%2F2
x=%282%2B-+4i%29%2F2
x=1%2B-+2i
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The zeros are 4, 1-2i, 1+2i.