Interesting Question!!
A quartic polynomial P(x) satisfies the following properties.
(A) P(3)=32
(B) P(2x+1)=16P(x+1) for all real x .
Then, find P(4).
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Answers
Answered by
0
Step-by-step explanation:
p(3)= 32
p(2x+1) = 16 p( x+1)
p(4)= p(3) +p(1)
= 32 + p(2×0+1) = 32 + 16 ×p(0+1)
= 32 + 16× p(1)
here, p(1) =?
p(3) = p( 2×1 +1) = 16×p(2)=..
Answered by
5
We know that we can find the value of by direct substitution of .
By factor theorem, is a factor of .
So let us assume,
By assumption,
For any real ,
As satisfies the equation,
By substituting ,
Since and are both a quartic polynomial, is a constant term.
Let us assume .
By assumption,
Hence,
And hence,
This is our answer.
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