Question

The polynomial p(x)=x^3+2x-11 has a real zero between which two consecutive integers?

Answer 1

Given:
p(x) = x³ + 2x - 11

Create a table of p(x) versus x for integral values of x from -2 to 2.
x p(x)
--- -------
-2 -23
-1 -14
0 -11
1 -8
2 1

A change in sign occurs for p(x) in the interval 1 ≤ x ≤ 2.
Therefore a real zero exists in this interval.

Answer: Between 1 and 2.
A real zero of p(x) occurs between x = 1 and x = 2.