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1 answer:
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Answer:
neither
geometric progression
arithmetic progression
Step-by-step explanation:
Given:
sequences:
To find: which of the given sequence forms arithmetic progression, geometric progression or neither of them
Solution:
A sequence forms an arithmetic progression if difference between terms remain same.
A sequence forms a geometric progression if ratio of the consecutive terms is same.
For :
Hence,the given sequence does not form an arithmetic progression.
Hence,the given sequence does not form a geometric progression.
So, is neither an arithmetic progression nor a geometric progression.
For :
As ratio of the consecutive terms is same, the sequence forms a geometric progression.
For :
As the difference between the consecutive terms is the same, the sequence forms an arithmetic progression.
Answer:
f(x) = + 2x³ - 4x² - 6x + 3
Step-by-step explanation:
Note that radical zeros occur in conjugate pairs, thus
- 1 + is a zero then - 1 -
is also a zero
is a zero then -
is also a zero
Thus the corresponding factors are
(x - (- 1 + ) ), (x - (- 1 -
) ), (x -
), (x - (-
)), that is
(x + 1 - ), (x + 1 +
), (x -
), (x +
)
The polynomial is then the product of the roots
f(x) = (x + 1 - )(x + 1 +
)(x -
)(x +
)
= ((x + 1)² - ()²)((x² - (
)²)
= (x² + 2x + 1 - 2)(x² - 3)
= (x² + 2x - 1)(x² - 3) ← distribute
= - 3x² + 2x³ - 6x - x² + 3
= + 2x³ - 4x² - 6x + 3