Question

Salut, am nevoie de ajutor la ex. 1.348B( explicatii pas cu pas, va rog)

Answer 1

$f(x)= 2x^5+3x^4+5x^3+3x^2+6x+4 \\ \\ f(x) = 2(x-x_1)(x-x_2)(x-x_3)(x-x_4)(x-x_5)\\ \\ f(-1) = 2(-1-x_1)(-1-x_2)(-1-x_3)(-1-x_4)(-1-x_5) \\ \\ f(-1) = 2(1+x_1)(1+x_2)(1+x_3)(1+x_4)(-1-x_5) \\ \\ f(-1) = -2(1+x_1)(1+x_2)(1+x_3)(1+x_4)(1+x_5)\\ \\ -\dfrac{2}{f(-1)} = \dfrac{1}{1+x_1}\cdot \dfrac{1}{1+x_2}\cdot \dfrac{1}{1+x_3}\cdot \dfrac{1}{1+x_4}\cdot \dfrac{1}{1+x_5} \\ \\ \\-\dfrac{2}{f(-1)} =-\dfrac{2}{-2+3-5+3-6+4} = -\dfrac{2}{-3} = \dfrac{2}{3}$

=> c) corect.