Recordem: Equacions 2n grau incompletes

Una equació de 2n grau $a x^{2} + b x + c = 0$ és incompleta quan els coeficient b o c són zero

- Cas $b = 0$

$a x^{2} + c = 0$

$a x^{2} = - c \to x^{2} = - \frac{c}{a} \to x = \pm \sqrt{- \frac{c}{a}}$

Exemples

$4 x^{2} - 25 = 0 \to 4 x^{2} = 25 \to x^{2} = \frac{25}{4} \to x = \pm \sqrt{\frac{25}{4}} = \pm \frac{5}{2}$

$4 x^{2} + 25 = 0 \to 4 x^{2} = - 25 \to x^{2} = - \frac{25}{4} \to x = \pm \sqrt{- \frac{25}{4}} N o t é s o l u c i ó$

- Cas $c = 0$

$a x^{2} + b x = 0$

$x (a x + b) = 0 \to \{\begin{cases} x = 0 \\ a x + b = 0 \to a x = - b \to x = - \frac{b}{a} \end{cases}$

Exemples

$3 x^{2} + 5 x = 0 \to x (3 x + 5) = 0 \to \{\begin{cases} x = 0 \\ 3 x + 5 = 0 \to 3 x = - 5 \to x = - \frac{5}{3} \end{cases}$

$x^{2} - 5 x = 0 \to x (x - 5) = 0 \to \{\begin{cases} x = 0 \\ x - 5 = 0 \to x = 5 \end{cases}$