Question

determinati radacinile intregi ale polinomului f=x^3-2x^2-9x+18

Answer 1

 

$\displaystyle\\f=x^3-2x^2-9x+18\\\text{Aflarea radacinilor acestui polinom este echivalenta cu rezolvarea ecuatiei:}\\x^3-2x^2-9x+18=0\\\\\text{Rezolvare:}\\\\x^3-2x^2-9x+18=0\\\\(x^3-2x^2)-(9x-18)=0\\\\x^2(x-2)-9(x-2)=0\\\\(x-2)(x^2-9)=0\\\\(x-2)(x^2-3^2)=0\\\\(x-2)(x-3)(x+3)=0\\\\x-2=0~\implies~\boxed{x_1=2\in Z}\\\\x-3=0~\implies~\boxed{x_2=3\in Z}\\\\x+3=0~\implies~\boxed{x_3=-3\in Z}$