Respuesta :
Answer:
The answer is C
Step-by-step explanation:
The roots are −1.87938524, 0.34729635, 1.53208888, −1.87938524, 0.34729635, and 1.53208888. That's 6 roots, which is C.
According to the Fundamental Theorem of Algebra, 6 roots exist for the polynomial function.
What is the fundamental Theorem of Algebra?
Fundamental Theorem of Algebra states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers. The roots can have a multiplicity greater than zero.
Given polynomial function
[tex]f(x)=(x^{3}-3x+1 )^{2}[/tex]
It has [tex](x^{3} )^{2}[/tex] term in the given polynomial
The fundamental theorem of algebra guarantees that a polynomial equation has the same number of roots as its degree.
= 3 × 2
= 6
So, 6 roots exist for the polynomial function.
Find out more information about Fundamental Theorem of Algebra here
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