Determine which consecutive integers do not have a real zero of x^3+9x^2+23x+14 between them.

What exactly are they asking me to do in order to get the answer?

Question

Determine which consecutive integers do not have a real zero of x^3+9x^2+23x+14  between them.

What exactly are they asking me to do in order to get the answer?

phi · Answer

I assume they gave you a list of pairs of integers as your choices?

anonymous · Answer

yeah they did 
(-1,0)
(0,1)
(-5,-4)
(-4,-3)

phi · Answer

if so,  test each (x1 , x2) pair
if the expression at x1 has a different sign than at x2, it will cross the x-axis in between. There will be a zero between x1 and x2

you have to find the pair where there is NOT a zero.  i.e. where f(x1) and f(x2) have the same sign

anonymous · Answer

Oh, now I understand it! Thanks for the help. :)

phi · Answer

generally, if f(x1) has the same sign as f(x2)  that does not mean there is no zero in between, because it could be like this:
|dw:1385559718793:dw|

but in this problem, your highest exponent is 3  (on the x^3 term). That means there are only 3 roots.  They give you 3 intervals where the 3 roots are... so the 4th interval will not have a root.