Math Problem Statement

Consider the following function: g(x) = 3x^4 + 5x^3 - 5. Use the Intermediate Value Theorem and a graphing utility to find intervals where the polynomial is guaranteed to have a zero. Also, adjust the table to approximate the zeros of the function.

Solution

Let's break down the problem from the image:

Given:

The polynomial function ( g(x) = 3

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Math Problem Analysis

Mathematical Concepts

Polynomials
Intermediate Value Theorem
Root Finding

Formulas

g(x) = 3x^4 + 5x^3 - 5

Theorems

Intermediate Value Theorem

Suitable Grade Level

Grades 10-12 (Precalculus/Calculus)

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