Final answer:
The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b] and takes on two different values at the endpoints, then it must also take on every value between those two values at some point within the interval. In this case, the polynomial function f(x) = 2x^4 - 10x + 6 is continuous and takes on different values at -2 and 0, so it must have a real zero between -2 and 0.
Step-by-step explanation:
The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b] and takes on two different values at the endpoints, then it must also take on every value between those two values at some point within the interval.
In this case, we can apply the Intermediate Value Theorem to the polynomial function f(x) = 2x4 - 10x + 6, which is a continuous function.
Since f(-2) = 50 and f(0) = 6, and 0 is between -2 and 0, we can conclude that there must be a real zero of the polynomial between -2 and 0.