Vgln. tweede graad

Los op. Vermijd indien mogelijk het gebruik van de discriminant.

\(8x^2+\frac{25}{6}x+\frac{1}{2}=0\)

\(8x^2+\frac{25}{6}x+\frac{1}{2}=0\\ \Leftrightarrow \color{red}{6.} \left(8x^2+\frac{25}{6}x+\frac{1}{2}\right)=0 \color{red}{.6} \\ \Leftrightarrow 48x^2+25x+3=0 \\\text{We zoeken de oplossingen van } \color{blue}{48x^2+25x+3=0} \\ \\\begin{align} D & = b^2 - 4.a.c & & \\ & = (25)^2-4.48.3 & &\\ & = 625-576 & & \\ & = 49 & & \\ \\ x_1 & = \frac{-b-\sqrt{D}}{2.a} & x_2 & = \frac{-b+\sqrt{D}}{2.a} \\ & = \frac{-25-\sqrt49}{2.48} & & = \frac{-25+\sqrt49}{2.48} \\ & = \frac{-32}{96} & & = \frac{-18}{96} \\ & = \frac{-1}{3} & & = \frac{-3}{16} \\ \\ V &= \Big\{ \frac{-1}{3} ; \frac{-3}{16} \Big\} & &\end{align} \\ -----------------\)