Respuesta :
Polynomial is an expression consisting of indeterminates and coefficients, also mathematical operations. option 1 is a complete list of the roots of the polynomial function.
What are polynomial?
Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
As it is given that a polynomial function f(x) is a fourth-degree polynomial. Therefore, it must have 4 roots. Now if we check all the options for the possible list of roots of f(x).
Looking at the options,
Option 1. 3,4,5,6 can be the complete list for polynomial function f(x).
Now, Option 2 and option 3 cannot be the complete list of the roots for f(x) as it has one complex root and complex roots always occur in pairs.
Further, Option 4 cannot be the complete list for f(x) as complex roots occur in pairs and they conjugates but conjugate of 5+i is 5-i(which is not given), not -5+i.
Hence, option 1 is a complete list of the roots of the polynomial function.
Learn more about Polynomial:
https://brainly.com/question/17822016
