Question

Salut, ma puteti ajuta la problema 16...?

Answer 1

Am atasat rezolvarea!

Raspuns E.

Answer 2

$P(x) = x^3+3x+2\\ \\ \text{Notam G(x) polinomul cu radacinilem:}~~1+x_1, 1+x_2, 1+x_3.\\ \\G(x) = x^3 - S_1x^2+S_2x-S_3\\ \\S_1 = 1+x_1+1+x_2+1+x_3 = 3+x_1+x_2+x_3 = \\ =3+0 = 3 \\ \\ S_2 = (1+x_1)(1+x_2)+(1+x_1)(1+x_3)+(1+x_1)(1+x_3)\\ \\ P(x) = (x-x_1)(x-x_2)(x-x_3)$

$P'(x) = (x-x_1)(x-x_2)+(x-x_1)(x-x_3)+(x-x_2)(x-x_3)\\ \\ P'(-1) = (-1-x_1)(-1-x_2)+\\ +(-1-x_1)(-1-x_3)+(-1-x_2)(-1-x_3) =\\ = (1+x_1)(1+x_2)+(1+x_1)(1+x_3)+(1+x_1)(1+x_3)\Rightarrow \\ \\ \Rightarrow S2 = P'(-1) = 6\\ \\ S3 = (1+x_1)(1+x_2)(1+x_3) = -P(-1) = 2\\ \\ \\\Rightarrow G(x) = x^2-3x^2+6x-2$