Recordem

$$\begin{gathered} a{x}^2+bx+c=0 (a\ne 0) \\ \mathit{x}\mathbf{=}\frac{\mathbf{-}\mathbf{b}\mathbf{\pm }\sqrt{{\mathbf{b}}^{\mathbf{2}}\mathbf{-}\mathbf{4}\mathbf{a}\mathbf{c}}}{\mathbf{2}\mathbf{a}} \end{gathered}$$

Exemple 1

$$\begin{gathered} 2x^2+3x-2=0 \\ x=\frac{-3\pm \sqrt{(-3{)}^2-4·2·(-2)}}{2·2}=\frac{-3\pm \sqrt{9+16}}{4}=\frac{-3\pm \sqrt{25}}{4}=\frac{-3\pm 5}{4}=\left\{\begin{array}{l}\frac{-3+5}{4}=\frac{2}{4}=\frac{1}{2}\\ \frac{-3-5}{4}=\frac{-8}{4}=-2\end{array}\right. \end{gathered}$$

Exemple 2

$$\begin{gathered} 2x^2-3x-2=0 \\ x=\frac{-(-3)\pm \sqrt{(-3{)}^2-4·2·(-2)}}{2·2}=\frac{3\pm \sqrt{9+16}}{4}=\frac{3\pm \sqrt{25}}{4}=\frac{3\pm 5}{4}=\left\{\begin{array}{l}\frac{3+5}{4}=\frac{8}{4}=2\\ \frac{3-5}{4}=\frac{-2}{4}=-\frac{1}{2}\end{array}\right. \end{gathered}$$

Exemple 3

$$\begin{gathered} x^2-5x+6=0 \\ x=\frac{-(-5)\pm \sqrt{(-5{)}^2-4·1·6}}{2·1}=\frac{5\pm \sqrt{25-24}}{2}=\frac{5\pm \sqrt{1}}{2}=\frac{5\pm 1}{2}=\left\{\begin{array}{l}\frac{5+1}{2}=\frac{6}{2}=3\\ \frac{5-1}{2}=\frac{4}{2}=2\end{array}\right. \end{gathered}$$

Exemple 4

$$\begin{gathered} x^2-5x+7=0 \\ x=\frac{-(-5)\pm \sqrt{(-5{)}^2-4·1·7}}{2·1}=\frac{5\pm \sqrt{25-28}}{2}=\frac{5\pm \sqrt{-3}}{2} No té solució \end{gathered}$$