College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Find the zeros of the given function.

[tex]f(x) = 3x^4 - 13x^3 - 56x^2 + 164x - 48[/tex]

Answer :

To find the zeros of the function [tex]\( f(x) = 3x^4 - 13x^3 - 56x^2 + 164x - 48 \)[/tex], we need to determine the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 0 \)[/tex].

1. Identify the Polynomial:
The function given is a fourth-degree polynomial:
[tex]\[
f(x) = 3x^4 - 13x^3 - 56x^2 + 164x - 48
\][/tex]

2. Finding Zeros:
The zeros of [tex]\( f(x) \)[/tex] are the solutions to the equation [tex]\( f(x) = 0 \)[/tex]. Using algebraic techniques, such as synthetic division, factoring, or numerical methods, we find that the zeros of this polynomial are:

- [tex]\( x = -4 \)[/tex]
- [tex]\( x = \frac{1}{3} \)[/tex]
- [tex]\( x = 2 \)[/tex]
- [tex]\( x = 6 \)[/tex]

3. Verification:
You can verify these solutions by substituting each zero back into the polynomial and checking that it equates to zero, thus confirming these values are indeed the correct zeros of [tex]\( f(x) \)[/tex].

By following these steps, we find the zeros of the function are [tex]\( x = -4, \frac{1}{3}, 2, \)[/tex] and [tex]\( 6 \)[/tex].