Respuesta :
According to the Fundamental Theorem of Algebra, the number of roots of a polynomial is equal to the degree of the polynomial. The degree of the polynomial is the highest exponent of a term in the polynomial.
Looking at the function, the term with the highest exponent is 8x7. The exponent is 7; therefore, the function has 7 roots.
Looking at the function, the term with the highest exponent is 8x7. The exponent is 7; therefore, the function has 7 roots.
According to the Fundamental Theorem of Algebra, the roots exist for the polynomial function [tex]f\left( x \right) = 8{x^7} - {x^5} + {x^3} + 6 x[/tex] is [tex]\boxed7.[/tex]
Further explanation:
The Fundamental Theorem of Algebra states that the polynomial has n roots if the degree of the polynomial is n.
[tex]f\left( x \right) = a{x^n} + b{x^{n - 1}} +\ldots + cx + d[/tex]
The polynomial function has n roots or zeroes.
Degree is highest power of the polynomial function.
Given:
The polynomial function is [tex]f\left( x \right) = 8{x^7} - {x^5} + {x^3} + 6.[/tex]
Explanation:
The polynomial function [tex]f\left( x \right) = 8{x^7} - {x^5} + {x^3} + 6[/tex] has seven zeroes as the degree of the polynomial is 7.
According to the Fundamental Theorem of Algebra, the roots exist for the polynomial function [tex]f\left( x \right) = 8{x^7} - {x^5} + {x^3} + 6[/tex] is [tex]\boxed7.[/tex]
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
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, seven roots.
