Question

The polynomial function f(x) = 5x^5 + 16/5x - 3 is graphed below. Which is a potential rational root of f(x) at point P?

A) the root at point P may be 3/5.
B) The root at point P may be 1/5.
C) The root at point P may be 5/3.
D) The root at point P may be 1/3.

Answer 1

The potential rational root of the polynomial function at point P is 1/3.

Step-by-step explanation:

The polynomial function f(x) = 5x5 + 16/5x - 3 can be simplified as follows:

1. Multiply the constant term, 16/5, by the leading coefficient, 5, to get 16x.
2. Combine like terms to get the final simplified polynomial: f(x) = 5x5 + 16x - 3.

To find the potential rational root at point P, we need to solve the equation f(x) = 0. Let's set the equation equal to zero:

5x5 + 16x - 3 = 0

We can use synthetic division or a graphing calculator to find the potential rational roots. From the graph, it appears that the root at point P may be 1/3. Therefore, the correct answer is D) The root at point P may be 1/3.

Polynomial functions are widely used in mathematics and science to model various phenomena, and they have important applications in fields such as physics, engineering, computer science, and more. The study of polynomials involves understanding their properties, roots, and behaviors.