Applying the First Theorem on Bounds for Real Zeros of Polynomials

Multiple Choice

Applying the first theorem on bounds for real zeros of polynomials, determine the smallest and largest integers that are upper and lower bounds, respectively, for the real solutions of the equation. With the aid of a graphing utility, discuss the validity of the bounds. $$3 x ^ { 4 } - 7 x ^ { 3 } - 5 x - 6 = 0$$

A) The upper bound is $$5$$ , the lower bound is $- 3$ .
B) The upper bound is $3$ , the lower bound is $- 1$ .
C) The upper bound is $0$ , the lower bound is $- 2$ .
D) The upper bound is $1$ , the lower bound is $$- 3$$ .
E) The upper bound is $2$ , the lower bound is $- 4$ .