Construct a polynomial function of least degree possible using the given information.
1 answer:
Answer:
f(x) = (-5/3)x³ +5x² +(5/3)x -5
Step-by-step explanation:
For root "a", the polynomial will have a factor (x -a). Given the three roots, the polynomial will be the product of the three factors ...
... p(x) = (x +1)(x -1)(x -3)
The value of p(2) is 3·1·(-1) = -3. In order to make f(2) = 5, we need to multiply p(x) by -5/3.
... f(x) = (-5/3)p(x)
... f(x) = (-5/3)(x +1)(x -1)(x -3)
Expanding gives
... f(x) = (-5/3)x³ +5x² +(5/3)x -5
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The recursive formula for given sequence is:
And the terms will be expressed as:
Step-by-step explanation:
First of all, we have to determine if the given sequence is arithmetic sequence or geometric. For that purpose, we calculate the common difference and common ratio
Given sequence is:
11,4,-3,-10,-17...
Here
As the common difference is same, given sequence is an arithmetic sequence.
A recursive formula is a formula that is used to generate the next term of the sequence using the previous term and common difference
So, the recursive formula for an arithmetic sequence is given by:
Hence,
The recursive formula for given sequence is:
And the terms will be expressed as:
Keywords: arithmetic sequence, common difference
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