Question

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = 8x7 – x5 + x3+6

Answer 1

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.

Answer 2

According to the Fundamental Theorem of Algebra, the roots exist for the polynomial function $f\left( x \right) = 8{x^7} - {x^5} + {x^3} + 6 x$ is $\boxed7.$

Further explanation:

The Fundamental Theorem of Algebra states that the polynomial has n roots if the degree of the polynomial is n.

$f\left( x \right) = a{x^n} + b{x^{n - 1}} +\ldots + cx + d$

The polynomial function has n roots or zeroes.

Degree is highest power of the polynomial function.

Given:

The polynomial function is $f\left( x \right) = 8{x^7} - {x^5} + {x^3} + 6.$

Explanation:

The polynomial function $f\left( x \right) = 8{x^7} - {x^5} + {x^3} + 6$ 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 $f\left( x \right) = 8{x^7} - {x^5} + {x^3} + 6$ is $\boxed7.$

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 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.