Question

A equação 2x^3 -5x^2 -x + 6 =0 admite uma raiz igual a 2. Então, as outras duas raízes são?

Answer 1

$\mathrm{2x^3-5x^2-x+6=0\ \to\ a=2}\\\\ \mathbf{Pelo\ m\acute{e}todo}\ \textbf{de\ Briot-Ruffini,\ teremos\ que:}\\\\ \mathrm{\ \ \ \ +2\ \ -5\ \ -1\ \ +6}\\ \mathrm{+2\ \ \ \ \ \ +4\ \ -2\ \ -6}\\ \mathrm{\ \ \ \ +2\ \ -1\ \ -3\ \ \ \ 0\ \ \ \ \to\ \ \ \boxed{\mathrm{2x^2-x-3=0}}}\\\\ \mathbf{Pela\ f\acute{o}rmula\ quadr\acute{a}tica,}\ \textbf{teremos que:} \\\\ \mathrm{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-1)\pm\sqrt{(-1)^2-4.2.(-3)}}{2.2}=}\\\\ \mathrm{=\dfrac{1\pm\sqrt{1+24}}{4}=\dfrac{1\pm\sqrt{25}}{4}=\dfrac{1\pm5}{4}=\boxed{\dfrac{3}{2}}\ ou\ \boxed{-1}}$