Option (D) is correct as the polynomial has exactly 6 roots according to the Fundamental Theorem of Algebra.
Further explanation:
The Fundamental Theorem of Algebra states that the polynomial has n roots if the degree of the polynomial is n.
The polynomial function has n roots or zeroes.
Given:
The polynomial functions are as follows.
(a).
(b).
(c).
(d).
Explanation:
The polynomial has maximum 4 roots as the degree of the polynomial is 4.
Hence, option (a) is not correct.
The polynomial has maximum 5 roots as the degree of the polynomial is 5.
Hence, option (b) is not correct.
The polynomial + x – 5 has maximum 5 roots as the degree of the polynomial is 5.
Hence, option (c) is not correct.
The polynomial has maximum 6 roots as the degree of the polynomial is 6.
Hence, Option (d) is correct as the polynomial has exactly 6 roots according to the Fundamental Theorem of Algebra.
Learn more:
1. Learn more about inverse of the function <u>brainly.com/question/1632445.
</u>
2. Learn more about equation of circle <u>brainly.com/question/1506955.
</u>
3. Learn more about range and domain of the function <u>brainly.com/question/3412497
</u>
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Polynomials
Keywords: quadratic equation, equation factorization. Factorized form, polynomial, quadratic formula, zeroes, Fundamental Theorem of algebra, polynomial, six roots.