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horrorfan [7]
3 years ago
12

Which of the following is a polynomial with roots 5, 4i, and -4i?

Mathematics
1 answer:
solniwko [45]3 years ago
8 0

The correct answer is x^3 - 5x^2 + 16x - 80.

In order to find this, we work backwards. Start by creating true statements for each of the roots.

x = 5

x = +/-4i

Now we can solve all of these until they are statements that equal 0.

x = 5 ----> Subtract 5 from both sides

x - 5 = 0

x = +/-4i ------> Square both sides

x^2 = -16 ---> Add 16 to both sides.

x^2 + 16 = 0

Now we can use the two statements that we have and multiply them to get the polynomial.

(x - 5)(x^2 + 16)

x^3 - 5x^2 + 16x - 80

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Brandon has a playlist with 83 hip-hop and pop songs. There are 15 more hip-hop songs than pop songs. How many pop songs are on
kogti [31]

Using a system of equations, it is found that there are 34 pop songs are on the playlist.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

  • Variable x: Number of hip-hop songs.
  • Variable y: Number of pop songs.

Brandon has a playlist with 83 hip-hop and pop songs, hence:

x + y = 83.

There are 15 more hip-hop songs than pop songs, hence:

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Replacing the second onto the first equation:

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There are 34 pop songs are on the playlist.

More can be learned about a system of equations at brainly.com/question/24342899

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A car dealer sold a car for 120% of the base price. The car sold for 24000. What was the base price of the car
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The correct answer is 19,200. Hope this helps. :)
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Read 2 more answers
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