SOLUTION: Show that the given values are zeros of P(x) and find all other zeros. P(X)=3x^4-8x^3-14x^2+31x+6 Values: -2 and 3

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Show that the given values are zeros of P(x) and find all other zeros. P(X)=3x^4-8x^3-14x^2+31x+6 Values: -2 and 3      Log On


   

Question 1127451: Show that the given values are zeros of P(x) and find all other zeros.
P(X)=3x^4-8x^3-14x^2+31x+6 Values: -2 and 3
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
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Show that the given values are zeros of P(x) and find all other zeros.
P(X)=3x^4-8x^3-14x^2+31x+6 Values: -2 and 3
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-2   |   3   -8   -14   31    6
     |
     |       -6    28  -28    -6
     |____________________________
         3  -14    14    3    0      -----remainder 0,  root:   -2


3   |   3   -14   14   3
    |
    |        9    -15  -3
    |______________________    
       3     -5   -1   0    ---------remainder 0, root:  +3

P%28x%29=%28x%2B2%29%28x-3%29%283x%5E2-5x-1%29

The quadratic roots
%285%2B-+sqrt%2825%2B12%29%29%2F6

These other two roots are therefore irrational,
%285-sqrt%2813%29%29%2F6
and
%285%2Bsqrt%2813%29%29%2F6