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) = 8x^7 - x^5 + x^3 + 6\n3 roots\n4 roots\n7 roots\n8 roots

according to the fundamental theorem of algebra, how many roots exist for the polynomial function?\nf(x) = 8x^7 - x^5 + x^3 + 6\n3 roots\n4 roots\n7 roots\n8 roots

Answer

Explanation:

Step1: Recall the fundamental theorem of algebra

The fundamental theorem of algebra states that the number of roots (counting multiplicities) of a non - zero polynomial (f(x)=a_nx^n + a_{n - 1}x^{n-1}+\cdots+a_1x + a_0) is equal to its degree (n), where (a_n\neq0).

Step2: Determine the degree of the polynomial

For the polynomial (f(x)=8x^7 - x^5+x^3 + 6), the highest - power of (x) is (7). So the degree (n = 7).

Answer:

7 roots