Question

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function f(x)=4x^5−3x

Answer 1

The polynomial function f(x)=4x^5-3x will have exactly 5 roots according to the Fundamental Theorem of Algebra because its degree is 5.

Step-by-step explanation:

According to the Fundamental Theorem of Algebra, every non-zero single-variable polynomial function of degree n has exactly n complex roots, including multiple and complex roots. This is true as long as roots are counted with their multiplicity. For the polynomial function f(x)=4x5−3x, the degree is 5. Therefore, this polynomial function has exactly 5 roots.