Three roots of a fifth degree polynomial function f(x) are –2, 2, and 4 + i. which statement describes the number and nature of all roots for this function? a. f(x) has two real roots and one imaginary root. b. f(x) has three real roots. c. f(x) has five real roots. d. has three real roots and two imaginary roots.

We are given

degree of polynomial =5

so, there must be five roots

we are given

roots of polynomial are

–2, 2, and 4 + i

We can see that one of root is 4+i

which is complex number

we know that

complex roots of any polynomial always exist in conjugate form

so, we will one more root which would be conjugate of 4+i

so, fifth root would be 4-i

so, two roots must be imaginary

since, we have total five roots

so, remaining roots must be real

Hence , option-DAnswer

D

Step-by-step explanation:

On edge

i dont know sorry

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9

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