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Which answer best describes the complex zeros of the polynomial function? f(x)=x^3−3x^2+16x−48
A The function has three nonreal zeros.
B The function has three real zeros.
C The function has two real zeros and one nonreal zero.
D The function has one real zero and two nonreal zeros.

Sagot :

Using the Factor Theorem, it is found that the correct option regarding the complex zeros of f(x) is given by:

D The function has one real zero and two nonreal zeros.

What is the Factor Theorem?

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

In this problem, the function is given by:

f(x) = x³ - 3x² + 16x + 48.

Using a calculator, the roots are given by:

[tex]x_1 = -1.89767, x_2 = 2.44884 + 4.39288i, x_3 = 2.44884 - 4.39288i[/tex]

The first root is real, while the second and third are complex(nonreal), hence option D is correct.

More can be learned about the Factor Theorem at https://brainly.com/question/24380382

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