VKV met breuken of rekenwerk

Gebruik de discriminant om volgende vierkantsvergelijkingen op te lossen

\(4x^2+\frac{15}{4}x-\frac{1}{4}=0\)

\(4x^2+\frac{15}{4}x-\frac{1}{4}=0\\ \Leftrightarrow \color{red}{4.} \left(4x^2+\frac{15}{4}x-\frac{1}{4}\right)=0 \color{red}{.4} \\ \Leftrightarrow 16x^2+15x-1=0 \\\text{We zoeken de oplossingen van } \color{blue}{16x^2+15x-1=0} \\ \\\begin{align} D & = b^2 - 4.a.c & & \\ & = (15)^2-4.16.(-1) & &\\ & = 225+64 & & \\ & = 289 & & \\ \\ x_1 & = \frac{-b-\sqrt{D}}{2.a} & x_2 & = \frac{-b+\sqrt{D}}{2.a} \\ & = \frac{-15-\sqrt289}{2.16} & & = \frac{-15+\sqrt289}{2.16} \\ & = \frac{-32}{32} & & = \frac{2}{32} \\ & = -1 & & = \frac{1}{16} \\ \\ V &= \Big\{ -1 ; \frac{1}{16} \Big\} & &\end{align} \\ -----------------\)