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MAVERICK [17]
3 years ago
11

Find a third-degree polynomial equation with the rational coefficients that has roots -3 and 1+i

Mathematics
1 answer:
jolli1 [7]3 years ago
3 0

Answer:

x³ + x² − 4x + 6 = 0

Step-by-step explanation:

Imaginary roots come in conjugate pairs.  So if 1+i is a root, then 1−i is also a root.

(x − (-3)) (x − (1+i) (x − (1−i)) = 0

(x + 3) (x² − (1+i) x − (1−i) x + (1+i) (1−i)) = 0

(x + 3) (x² − x − ix − x + ix + 1 − i²) = 0

(x + 3) (x² − 2x + 2) = 0

x (x² − 2x + 2) + 3 (x² − 2x + 2) = 0

x³ − 2x² + 2x + 3x² − 6x + 6 = 0

x³ + x² − 4x + 6 = 0

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If the least value of n is 4, which inequality best shows all the possible values of n?
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Comment
If the least value of n is 4 that means that 4 is one of the numbers in whatever it is that you are describing. In other words n = 4 is part of your answer. If that is the case, the last two values are incorrect because 4 is not included in either one of them.

Discussion
So that means that you have to choose between one of the first 2. The key word is least. It means that the lowest possible value is 4. Nothing is lower. 

When you write something like n ≤ 4 what you are saying is the n must be = to or less than 4. The arrow head points to the smallest number which, in this case, is n. 

But the question says that the least number is 4. So the arrowhead must point towards the 4. This we have that n must be larger than 4. 

Conditions
There are 2 conditions to this problem
n must be greater than 4
n can equal 4. It is the smallest number.

Answer
n≥4 <<<<<answer
B <<<<<< answer.
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4 years ago
9. The Strawberry Festival is finally here! Mrs.
chubhunter [2.5K]

\left \{ {{- \atop {2(21.5-2y)+2y=30}} \right.Answer:

Step-by-step explanation:

a)

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system will be:

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b)

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a box of strawberries is 6.5

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Students in biology are studying the macromolecules of life. They used a calorimeter to determine the calories in various types
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Answer:D

Step-by-step explanation:

The answer is D

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3 years ago
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