Question

Find an upper and lower limit for the zero of the following function. f(x)=x^3-3x^2-2x+15

Answer 1

The greatest integer lower bound for the zeros if f is -2; the least integerupper bound for the zeros of f is 4.

This theorem is sometimes called the Boundedness Theorem. For the sake of brevity I did not show the preceding synthetic divisions.

4 | 1 -3 -2 15
4 4 8
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1 1 2 23 entire bottom row is greater than or equal to 0

-2 | 1 -3 -2 15
-2 10 -16
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1 -5 8 -1 bottom row alternate in sign