what is the upper bound of X^4+2x^3-17x^2-13x+19

Question

trying to find upper and lower bound of the 0s

Answer 1

19 is a prime number.  Therefore, the only roots you can test are ±1 and ±19.

 

 

-19 | 1        2           -17         -13       19

 

                 -19       large +       -         +

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         1      -17          +            -          +

 

 

Signs alternate for negative root.  x=-19 is the lower bound

 

 

 

-1 | 1    2      -17         -13       19

 

            1        -3

______________________________

       1   3        -20

 

 

 

Signs are not alternating, we stop the process here for this root.

 

1 | 1    2      -17         -13       19

 

           1        3

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     1    3       -14

 

 

Signs are not the same.  We need them to be the same for positive roots.

 

 

19 | 1    2      -17         -13       19

 

            19       +           +          +

_______________________________

       1    21      +            +          +

 

 

The signs remains the same.

 

 

The zeros are in the interval (-19, 19).