f (x) = x5 − 8x4 + 21x3 − 12x2 − 22x + 20

Three roots of this polynomial function are −1, 1, and 3 + i.

Which of the following describes the number and nature of all the roots of this function?

f (x) has two real roots and one imaginary root.

f (x) has three real roots.

f (x) has five real roots.

f (x) has three real roots and two imaginary roots.

Question

04-12-2021
Mathematics

Answered

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f (x) = x5 − 8x4 + 21x3 − 12x2 − 22x + 20

Three roots of this polynomial function are −1, 1, and 3 + i.

Which of the following describes the number and nature of all the roots of this function?

f (x) has two real roots and one imaginary root.

f (x) has three real roots.

f (x) has five real roots.

f (x) has three real roots and two imaginary roots.

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sqdancefan sqdancefan · Answer 1 · 2021-12-04T23:07:36-05:00

Answer:

f(x) has three real roots and two imaginary roots.

Step-by-step explanation:

The function is degree 5, so will have 5 roots in total. 2 real roots and one complex root are shown. Complex roots come in pairs, so there will be one more, but cannot be two more.

f(x) has three real roots and two imaginary roots.

__

All five roots must be accounted for. This leaves out the first two choices. The given complex root eliminates the third choice.

qf9xe95zxe qf9xe95zxe · Answer 2 · 2022-04-10T23:36:12-04:00

qf9xe95zxe qf9xe95zxe

10-04-2022

Answer:

D

Step-by-step explanation:

did the test

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