Does this equation have two real zeroes? Why or why not? **Question: Analyzing the Polynomial Function**Does the function \( f(x) = -5x^4 + 6 \) have 2 real zeroes? Why or why not?**Explanation:**To determine whether the function \( f(x) = -5x^4 + 6 \) has two real zeroes, we need to consider the behavior and characteristics of the polynomial.1. **Degree and Leading Coefficient:** - The function is a quartic polynomial (degree 4) with a leading coefficient of -5. - A negative leading coefficient indicates the graph opens downward.2. **Even Degree Polynomials:** - Polynomials with an even degree and negative leading coefficients have endpoints that go to negative infinity as \( x \) approaches both positive and negative infinity.3. **Finding the Zeroes:** - Set \( f(x) = 0 \): \[ -5x^4 + 6 = 0 \implies 5x^4 = 6 \implies x^4 = \frac{6}{5} \] - Solve for \( x \) using the fourth root: \[ x = \pm \sqrt[4]{\frac{6}{5}} \] - Since there are positive and negative solutions, there are zeroes, but they are not necessarily real if considering the multiplicity in terms of sign.4. **Number of Real Zeroes:** - The quartic function \( x^4 = \frac{6}{5} \) results in real solutions for \( x \). - Since the function's degree is even and it opens downward, it could cross the x-axis at most twice, depending on the roots.Thus, the function can have 2 real zeroes, but analyzing further would involve calculating exact values and evaluating their impact on the graph. The presence of 2 or more real zeroes is corroborated by the even degree and behavior as described.

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Answered: 4 Does f(x) = -5x + 6 have 2 real…

4 Does f(x) = -5x + 6 have 2 real Zeroes? why not? why

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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