according to the fundamental theorem of algebra, how many roots exist for the polynomial function?\nf(x) =…

according to the fundamental theorem of algebra, how many roots exist for the polynomial function?\nf(x) = 4x^5 - 3x\n1 root\n2 roots\n4 roots\n5 roots

according to the fundamental theorem of algebra, how many roots exist for the polynomial function?\nf(x) = 4x^5 - 3x\n1 root\n2 roots\n4 roots\n5 roots

Answer

Explanation:

Step1: Recall the Fundamental Theorem of Algebra

The Fundamental Theorem of Algebra states that the number of roots of a polynomial function (f(x)=a_nx^n + a_{n - 1}x^{n-1}+\cdots+a_1x + a_0) (where (a_n\neq0)) is equal to its degree (n).

Step2: Determine the degree of the given polynomial

For the polynomial (f(x)=4x^5-3x), the highest - power of (x) is (n = 5). So the degree of the polynomial is 5.

Answer:

D. 5 roots