The Intermediate Value Theorem guarantees that the equation has a solution in the following interval:

Question

The Intermediate Value Theorem guarantees that the equation  has a solution in the following interval:

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The intermediate value theorem states that if a function f is continuous on a closed interval [a,b], then f takes on every value between f(a) and f(b). In the given equation, the left-hand side is a continuous function (polynomial) and it takes the value 0 at a (substituting 0 gives 11eaa655_3b5e_7b2d_a696_13daf5f720dc_TB5596_11), and it takes a positive value for a large positive value of x and a negative value for a large negative value of x. Therefore, by the intermediate value theorem, there must be a value of x in the interval [a,∞) for which the equation equals 0. Therefore, choice A is the best option.

The Intermediate Value Theorem Guarantees That the Equation Has