Determine which consecutive integers do not have a real zero of f (x) = x^3+5x^2 - x - 6 between them.

(-6,-5)

(-2,-1)

(-5,-4)

(1,2)

(-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.