Use the Imtermediate Value Theorem to determine whether the polynomial function has a real zero between?

Question

the given integers.

F(x) = 7x^3 + 10x + 3; between -1 and 0

Answer 1

Intermediate value theorem:
Suppose that f : [a,b] ---> R is continuous and that u is a real number satisfying f(a) < u < f(b) or f(a) > u > f(b). Then for some c є [a,b], f(c) = u.
Apply the Intermediate value theorem to this example:
f(-1) = 7(-1)^3 +10(-1) + 3 = -14
f(0) = 3
-14 < 0 < 3, so for some c є [-1, 0], f(c) = 0