Question

Fie polinomul f = X^3 -6X^2+11X-6 ∈ R[x] . Daca notam cu x1 , x2 ,x3 radacinile sale , calculati S = x1^2 + x2^2 + x3^2 . (nr 1,2,3 sunt sub forma de indice) .

Answer 1

[tex]S=x_1^2+x_2^2+x_3^2=(x_1+x_2+x_3)^2-2(x_1\cdotx_2+x_2\cdot x_3 +x_1\cdot x_3)\\ \text{Din relatiile lui Viete avem:}\\ S=6^2-2\cdot 11=36-22=14\\ \boxed{S=14} [/tex]