Question

Escreva a equação abaixo na forma fatorada
A) 2y²+4y-6=0

Answer 1

$\mathrm{2y^2+4y-6=0\ \to\ a=2\ \ \| \ \ b=4\ \ \| \ \ c=-6}\\ \mathrm{Forma\ fatorada\ \to\ a(y-y_1)(y-y_2)=0}\\\\ \mathbf{Calculando\ y_1\ e\ y_2\ (f\'ormula\ quadr\'atica):}\\\\ \mathrm{y=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-4\pm\sqrt{4^2-4.2.(-6)}}{2.2}=}\\\\ \mathrm{=\dfrac{-4\pm\sqrt{16+48}}{4}=\dfrac{-4\pm\sqrt{64}}{4}=\dfrac{-4\pm8}{4}=-1\pm2}\\\\ \mathrm{y_1=-1+2=1\ \ \| \ \ y_2=-1-2=-3\ \ \|\ \ \mathbf{\{1,-3\}}}$

$\textbf{Forma fatorada da equa\c{c}\~ao:}\\\\ \mathrm{2y^2+4y-6=0\ \to\ 2(y-1)(y-(-3))=0}\\ \mathrm{\boxed{\mathbf{2(y-1)(y+3)=0}}}$