Find the cubic polynomial satisfying f(0) = -5, f(1) = 0, f(2) = 15, f(3) = 52.?

[escobar147]

Here is the correct answer: 2x^3 - x^2 + 4x - 5

My attempt only gives me one cubed term and the other terms are also marginally off, any help on who can show me how to get the correct answer will be hugely appreciated

 

[Vargo]

Howdy,

What you need are Lagrange interpolation polynomials:
http://en.wikipedia.org/wiki/Lagrange_polynomial

 

[Norwegian]

Hi there,

What you really need is to translate the problem into a set of linear equations. If you let f(x)=ax³+bx²+cx+d, then f(0)=-5 gives d=-5, f(1)=0 gives a+b+c+d=0 etc, and you can quickly find the correct values of a, b, c and d.

 

[Vargo]

I guess it is a matter of taste as to whether one prefers to solve a system of linear equations or to just write down the answer.