According to the Fundamental Theorem of Algebra, how many roots does the polynomial function p(x)=5x2−3x3+6x5−4x4 have?(1 point) Responses 3 3 5 5 2 2 4 4

Answer 1

The Fundamental Theorem of Algebra states that a polynomial of degree \( n \) has exactly \( n \) roots (counting multiplicities) in the complex number system.

First, let's determine the degree of the polynomial \( p(x) = 5x^2 - 3x^3 + 6x^5 - 4x^4 \):

The terms are:

• \( 5x^2 \) (degree 2)
• \( -3x^3 \) (degree 3)
• \( 6x^5 \) (degree 5)
• \( -4x^4 \) (degree 4)

The term with the highest degree is \( 6x^5 \), which means the degree of the polynomial \( p(x) \) is 5.

According to the Fundamental Theorem of Algebra, a polynomial of degree 5 has exactly 5 roots.

Therefore, the answer is 5.