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Dovator [93]
2 years ago
12

F (x) = x5 − 8x4 + 21x3 − 12x2 − 22x + 20 Three roots of this polynomial function are −1, 1, and 3 + i. Which of the following d

escribes 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.
Mathematics
2 answers:
NeTakaya2 years ago
5 0

Answer:

It's D on edge.

mr Goodwill [35]2 years ago
3 0

Answer:

D.  

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

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2 years ago
A restaurant owner was experimenting with the taste of her homestyle lemon drink. She started with 60 litres of water. She remov
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Answer:

ratio of pure lemon juice to water in the homestyle lemon  drink is 5 : 19.

Step-by-step explanation:

In order to solve the final ratio of lemon juice to water, let us start by determining the initial ratio of pure lemon juice to water in the first mix. This is done as follows:

Total volume of mixture = 60 liters

initial volume of water = 60 liters

initial volume of lemon juice = 0 liters

1) She removed 15 liters of the water and replaced it with 15 liters of pure lemon juice.

Volume of water = 60 - 15 = 45 liters

Volume of lemon juice = 15 liters

 \therefore \frac{15}{60}\ = \frac{1}{4}\  of\ the\ first\ mix\ is\ lemon\ juice\\\frac{45}{60}\ = \frac{3}{4}\  of\ the\ first\ mix\ is\ pure\ water

2) She removed 10 liters of the new mixture

Let us convert this amount removed into ratio:

lemon\ juice\ = \frac{1}{4}\ \times 10 = \frac{10}{4} = \frac{5}{2}\ liters.\\  \therefore the\ owner\ removes\ \frac{5}{2}\ liters\ of\ pure\ lemon\ juice\\pure\ water\ = \frac{3}{4}\ \times 10 = \frac{30}{4} = \frac{15}{2}\ liters\\  \therefore\ the\ owner\ removes\ \frac{15}{2}\ liters\ of\ water\ from\ the\ first\ mix.

New volumes of water and lemon juice after removing the 10 liters of mixture is calculated as follows:

lemon\ juice\ = 15 - \frac{5}{2} = \frac{30-5}{2} = \frac{25}{2}\ liters\ of\ lemon\ juice\\pure\ water\ = 45 - \frac{15}{2} = \frac{90-15}{2} = \frac{75}{2}\ liters\ of\ pure\ water

3) and replaced it with 10 liters of water.

New\ volume\ of\ water\ = 10 + \frac{75}{2} = \frac{20+ 75}{2} = \frac{95}{2}\ liters

The final ratio of lemon juice to water:

\frac{25}{2} : \frac{95}{2}\\= 25 : 95\\= 5 : 19

Therefore, the final ratio of pure lemon juice to water in the homestyle lemon  drink is 5 : 19.

4 0
2 years ago
If y = 8x − 2, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs?
Nataly [62]
You just need to try with all of the pair f.ex
0,-2 -> put 0 in the x-> y=8*0-2=-2 so ok it is q possible pair of the function..
You try every pair till you find set where all the pairs fit
So set 1
1 and 6: 8*1-2=6 ok
2 and 14 : 8*2-2=14 ok
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The answer would be:

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0= 2/3x+1

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