Answer:
(-6, -5).
Step-by-step explanation:
If there is a zero between the integers there will be a change of sign of f(x).
x^3 + 5x^2 - x - 6
f(1) = 1 + 5 - 1 - 6 = -1
f(-1) = -1 + 5 + 1 - 6 = -1
f(2) = 8 + 20 - 2 -6 = 20
There' a change of sign between f(1) and f(2) so there is a zero between (1, 2).
f(-2) = -8 + 20 + 2 - 6= 6
So there is also a zero between -1 and -2. (-2, -1)
F(-4) = 14, f(-5) = -1 = change of sign so there is also a zero in (-5,-4)
f(-6) = -36 - no change in sign between -5 and -6.
