a_{0}a_{4}<0 so the two coefficients are of opposite sign. Let's assume a_{0}>0 for a second. Can you tell me where f(x) is positive? Also, two different places f(x) will be negative
That's not the requirement for f(x) to be positive, but that's OK. There's an easy to find value of x that makes f(x) positive. Think about how you would try to graph f(x) and you should see it