Answer
See below.
Work Step by Step
The Intermediate Value Theorem says that if a continuous (polynomials are always continuous) function on an interval [a,b] takes values $f(a)$ and $f(b)$ at the endpoints, then the function takes all values between $f(a)$ and $f(b)$ at some point of the interval.
Evaluate the function at the endpoints.
$f(-1)=6\cdot(-1)^2+5(-1)-6=6-5-6=-5.$
$f(2)=6\cdot(2)^2+5(2)-6=24+10-6=28.$
Since $-1\lt0\lt10$, according to the Intermediate Value Theorem, there must be a $0$ in the given interval.