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soldier1979 [14.2K]
3 years ago
9

Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ?

Mathematics
1 answer:
Alja [10]3 years ago
5 0

Using the factor theorem, it is found that the polynomial is:

f(x) = x^3 - 2x^2 - 3x + 6

Given by the first option

---------------------------

Given a polynomial f(x), this polynomial has roots x_{1}, x_{2}, x_{n} using the factor theorem it can be written as: a(x - x_{1})*(x - x_{2})*...*(x-x_n), in which a is the leading coefficient.

---------------------------

In this question:

  • x_1 = 2
  • x_2 = \sqrt{3}
  • x_3 = -\sqrt{3}
  • By the options, leading coefficient a = 1

Thus:

f(x) = (x - 2)(x - \sqrt{3})(x + \sqrt{3})

f(x) = (x - 2)(x^2 - 3)

f(x) = x^3 -2x^2 - 3x + 6

Which is the polynomial.

A similar problem is given that: brainly.com/question/4786502

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