Question

Resolva 2x3−8x2−10x=0 por fatoração. Insira as resoluções da menor para a maior.

Answer 1

$2x^3-8x^2-10x=0 \\ \\ fatorar~~sendo~~2x~~fator~~comum \\ \\ 2x(x^2-4x-5)=0 \\ \\ 2x=0 \\\fbox{ x_1=0 }$~

$x^2-4x-5=0 \\ \\ a=1 \\ b=-4 \\ c=-5 \\ \\ \Delta=b^2-4ac \\ \Delta=(-4)^2-4(1)(-5) \\ \Delta=16+20 \\ \Delta=36 \\ \\ x= \frac{-b\pm \sqrt{\Delta} }{2a} \\ \\ x= \frac{-(-4)\pm \sqrt{36} }{2} = \frac{4\pm6}{2} \\ \\ x_2= \frac{4+6}{2} = \frac{10}{2} =5 \\ \\ x_3= \frac{4-6}{2} =- \frac{2}{2} =-1 \\ \\ S=\{-1,0,5\}$