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Leona [35]
2 years ago
13

Three roots of a fifth degree polynomial function f(x) are –2, 2, and 4 i. Which statement describes the number and nature of al

l roots for this function?.
Mathematics
1 answer:
bagirrra123 [75]2 years ago
3 0

The correct option is f(x) has three real roots and two imaginary roots.

Given

Three roots of a fifth-degree polynomial function f(x) are –2, 2, and 4 i.

<h3>Complex conjugate</h3>

The complex conjugate of a complex number is the number with an equally real part and an imaginary part equal in magnitude but opposite in sign.

It is given that the roots of the fifth-degree polynomial function are -2, 2, and 4+i.

Since the degree of f(x) is 5, therefore there are 5 roots of the function either real or imaginary.

According to the complex conjugate root theorem, if a+ib is a root of a polynomial function f(x), then a-ib is also a root of the polynomial f(x).

Since 4+i is a root of f(x), so by complex conjugate rot theorem 4-i is also a root of f(x).

From the given data the number of real roots is 2 and the number of 2. The number of complex roots is always an even number, so the last root must be a real number.

Therefore, the correct option is f(x) has three real roots and two imaginary roots.

To know more about imaginary roots click the link given below.

brainly.com/question/1375079

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A 24 ft ladder is positioned next to a house for window cleaning. The manufacturer recommends the ladder rest at an angle of 76°
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Answer: ...

Step-by-step explanation:

8 0
2 years ago
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It took an hour to now a lawn using a mower with 14 inches blade. How long will it take using a mower with 12 inches wide
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If the time taken by 14 inches wide is one hour then the blade of 12 inches wide will take 1 hour 17 minutes to mow a lawn.

What is width?

The width of something is the measurement of one side of a body. It is generally less than length of that body or shape.

How to calculate time?

We have been given time of 1 hour if blade is 14 inches wide and we have to calculate time taken by 12 inches wide blade:

It will be as 14/12* 1 hour

=14/12

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Hence the time taken by the blade of 12 inches wide will be 1 hour and 17 minutes.

7 0
1 year ago
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steposvetlana [31]
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