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SUMMARY

The discussion centers on the interpolation of a polynomial given specific data points: $f(5)=?, f(8)=14, f(12)=214$. The interpolating polynomial is confirmed as $4.125x^{2}-32.5x+10$. The Newton form of the polynomial is expressed as $p_{2}(x)=a_{0}+a_{1}(x-5)+a_{2}(x-5)(x-3)$. The value of $a_{2}$ is definitively identified as 4.125, confirming the equivalence of the two polynomial forms.

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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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