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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
 

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