Determine which consecutive integers do not have a real zero of between them. a. (–6, –5) c. (–2, –1) b. (–5, –4) d. (1, 2) Please select the best answer from the choices provided A B C D
We have by the intermediate value theorem that if a continuous function takes values both above and below zero at 2 points, there is a zero of the function in-between. We have that polynomials are continues. Let's calculate f(-6) and f(-5). f(-6)=-36 while f(-5)=-1. Thus, we cannot conclude that there is a root between them. F(-2)=8, f(-1)=-1, so there is a flip; a zero must exist between them. F(1)=-1, f(2)=20, so again there is a change of signs. f(-5)=-1, f(-4)=14 so there is a root still. We have that the only choice that does not have a root between the integers is choice a.
