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The discussion centers on finding the value of \( a_2 \) in the Newton form of an interpolating polynomial given specific data points. The polynomial provided is \( 4.125x^{2} - 32.5x + 10 \), and the question arises whether \( a_2 \) equals 4.125. Participants confirm that the value of \( a_2 \) is indeed 4.125, affirming the equality of the two polynomial forms. The conversation concludes with expressions of gratitude for the clarification.
evinda
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Hello! :)

The interpolating polynomial that interpolates at the following data:
$f(5)=?,f(8)=14,f(12)=214$ is $4,125x^{2}-32,5x+10$.
The corresponding interpolating polynomial in the Newton form is $p_{2}(x)=a_{0}+a_{1}(x-5)+a_{2}(x-5)(x-3)$.Which is the value of $a_{2}$?
Is it 4,125 because the two polynomials should be equal or am I wrong? :confused:
 
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evinda said:
Hello! :)

The interpolating polynomial that interpolates at the following data:
$f(5)=?,f(8)=14,f(12)=214$ is $4,125x^{2}-32,5x+10$.
The corresponding interpolating polynomial in the Newton form is $p_{2}(x)=a_{0}+a_{1}(x-5)+a_{2}(x-5)(x-3)$.Which is the value of $a_{2}$?
Is it 4,125 because the two polynomials should be equal or am I wrong? :confused:

Yep. You are right! :D
 
I like Serena said:
Yep. You are right! :D

Great!Thank you very much! :o
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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