## College Algebra (10th Edition)

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. $f(0)=8\cdot0^4-4\cdot0^3-2\cdot0-1=0-0+0-1=-1.$ $f(1)=8\cdot1^4-4\cdot1^3-2\cdot1-1=8-4-2-1=1.$ Since $-1\lt0\lt1$, according to the Intermediate Value Theorem, there must be a $0$ in the given interval.