Wiskundeleraar

meer voorbeelden

Voorbeeld 1

$\eqalign{
& - 9{x^2} - 3x + 5 = 0 \cr
& 9{x^2} + 3x - 5 = 0 \cr
& a = 9,\,\,b = 3\,\,en\,\,c = - 5 \cr
& D = {3^2} - 4 \cdot 9 \cdot - 5 = 9 + 180 = 189 \cr
& x = \frac{{ - 3 \pm \sqrt {189} }}{{2 \cdot 9}} = \frac{{ - 3 \pm 3\sqrt {21} }}{{18}} \cr
& x = - \frac{1}{6} - \frac{1}{6}\sqrt {21} \vee x = - \frac{1}{6} + \frac{1}{6}\sqrt {21} \cr} $

Voorbeeld 2

$\eqalign{
& 2{x^2} + x - 6 = 0 \cr
& a = 2,\,\,b = 1\,\,en\,\,c = - 6 \cr
& D = {1^2} - 4 \cdot 2 \cdot - 6 = 1 + 48 = 49 \cr
& x = \frac{{ - 1 \pm \sqrt {49} }}{{2 \cdot 2}} = \frac{{ - 1 \pm 7}}{4} \cr
& x = \frac{{ - 8}}{4} = - 2 \vee x = \frac{6}{4} \cr
& x = - 2 \vee x = 1\frac{1}{2} \cr} $

Alternatieve oplossing

$\eqalign{
& 2{x^2} + x - 6 = 0 \cr
& 2{x^2} + 4x - 3x - 6 = 0 \cr
& 2x(x + 2) - 3(x + 2) = 0 \cr
& (2x - 3)(x + 2) = 0 \cr
& 2x - 3 = 0 \vee x + 2 = 0 \cr
& 2x = 3 \vee x = - 2 \cr
& x = 1\frac{1}{2} \vee x = - 2 \cr} $