Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

1. According to the fundamental theorem of algebra, how many zeros does the function [tex]f(x) = 3x^6 - 7x^5 - 53x^3 - 43x - 34[/tex] have?

2. What are the zeros of [tex]f(x) = 6x^3 + 25x^2 - 24x + 5[/tex]

Sagot :

Answer:

See below for answers

Step-by-step explanation:

1) The Fundamental Theorem of Algebra states that in an nth-degree polynomial, there are n zeroes at most, including those that are complex. Therefore, there are 6 zeroes in the function since it's a 6th-degree polynomial.

2) Reduce the polynomial and use the Zero Product Property:

[tex]0=6x^3+25x^2-24x+5[/tex]

[tex]0=(6x^2-5x+1)(x+5)[/tex]

[tex]0=(3x-1)(2x-1)(x+5)[/tex]

[tex]x_1=\frac{1}{3},x_2=\frac{1}{2},x_3=-5[/tex]

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.