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A polynomial function h(x) has a zero of x = 2 – 5i with a multiplicity of one. Certain values of h(x) are given in the following table.

x h(x)
–5 0
–2 3
–1 –1
1 2
4 0
7 6
10 5

If every real x-intercept of h(x) is shown in the table and each has a multiplicity of one, what is the degree of h(x)?
A. 2
B. 3
C. 4
D. 5

Respuesta :

The answer is 4! So c

Using function concepts, it is found that the degree of the function is: 4, option C.

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  • The x-intercepts of a function are the values of the function for which the output is zero.
  • The degree of a function is the sum of the multiplicities of the x-intercepts of the function.
  • If a function has a complex root, it means that the conjugate is also a root.

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  • When [tex]x = -5, h(x) = 0[/tex], thus, x = -5 is one x-intercept.
  • When [tex]x = 4, h(x) = 0[/tex], thus, x = 4 is one x-intercept.
  • There is also a x-intercept(zero) at [tex]x = 2 - 5i[/tex]. There will also be a x-intercept at the conjugate, which is [tex]x = 2 + 5i[/tex].
  • Thus, there are 4 x-intercepts, all with multiplicity 1, which means that the degree of h(x) is 4, option C.

A similar problem is given at https://brainly.com/question/10539060

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