No problem! Always happy to help with math questions.

In summary, the value of $a_{2}$ in the corresponding interpolating polynomial in the Newton form is 4,125, as the two polynomials should be equal.
  • #1
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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  • #2
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
 
  • #3
I like Serena said:
Yep. You are right! :D

Great!Thank you very much! :eek:
 

Related to No problem! Always happy to help with math questions.

1. What is a polynomial in Newton form?

A polynomial in Newton form is a way of representing a polynomial equation using the binomial coefficients and the divided difference operator. It is written as: f(x) = a0 + a1(x-x0) + a2(x-x0)(x-x1) + ... + an(x-x0)(x-x1)...(x-xn-1).

2. How is a polynomial in Newton form different from other forms?

A polynomial in Newton form is different from other forms, such as standard or factored form, because it does not require knowledge of the roots of the equation. It can be written using only the coefficients and the divided difference operator, making it a more efficient way to represent polynomial equations.

3. What is the divided difference operator?

The divided difference operator is a mathematical operation that is used in Newton's method of interpolation. It is used to calculate the coefficients of a polynomial in Newton form and is written as: f[xi,xj,...,xk] = (f[xj,...,xk] - f[xi,...,xk-1]) / (xk - xi).

4. How is a polynomial in Newton form useful?

A polynomial in Newton form is useful because it allows for efficient computation of polynomial equations, especially when dealing with large or complex equations. It also allows for easy addition or subtraction of terms, making it a useful tool in solving mathematical problems.

5. Can any polynomial equation be written in Newton form?

Yes, any polynomial equation can be written in Newton form. However, some equations may have more efficient forms for calculation, so it is important to consider the purpose of using Newton form before converting an equation to this form.

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