Question

Approximate the real number solution(s) to the polynomial function f(x) = x^3 + 4x^2 + x − 6.

a. x = −3, x = −1, x = 2
b. x = 3, x = 1, x = −2
c. x = 3, x = −1, x = 2
d. x = −3, x = 1, x = −2

Answer 1

d. x ∈ {-3, -2, 1}

Explanation:

The word "approximate" in the problem statement suggests that the roots may not be integers. Consequently, the solution method of choice is graphing.

A graph shows the solutions to f(x)=0 to be x=-3, x=-2, and x=1, matching selection D.

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Comment on the problem statement

Any value of x can be put into the formula and it will be a "solution." For example, f(0) = -6 is a "solution" to the polynomial function. The problem statement is not specific as to the solution(s) sought. We have had to guess that we want values of x such that f(x)=0.