contestada

Let (x1, y1),(x2, y2),(x3, y3) be points with distinct x-values. Prove there exists a polynomial p(x) of degree at most 2 passing through these points. State and prove a similar result for four points?

Respuesta :

facundo3141592

Answer: we can use the folowing polynomial.

P(x) = [tex]\frac{y1 (x - x2)(x -x3)}{(x1 - x2)(x1-x3)}[/tex] + [tex]\frac{y2 (x - x1)(x -x3)}{(x2 - x1)(x1-x3)}[/tex] + [tex]\frac{y3 (x - x2)(x -x1)}{(x3 - x2)(x3-x1)}[/tex]

you can see that P(x1) = y1

                          P(x2) = y2

                          P(x3) = y3

this is a Lagrange polynomial.

Otras preguntas