Question

Encontre, se existirem, as raízes reais da equação dada:
a) 2x 2+ 4x -1= 0

Answer 1

$2x^2+ 4x -1= 0\\ \\ \Delta=b^2-4.a.c\\ \Delta=4^2-4.2.(-1)\\ \Delta=16+8\\ \Delta=24\\ \\ x=\frac{-b\pm \sqrt{\Delta}}{2a}\\ \\ x=\frac{-4\pm\sqrt{24}}{2.2}=\frac{-4\pm2\sqrt6}{4}=\frac{-2\pm\sqrt6}{2}\\ \\ S=\{\frac{-2\pm\sqrt6}{2}\}$