Équation: $ax^2 + bx + c=0$ Discriminant: $\Delta = b^2 - 4ac$ $\Delta \lt 0 : S=\{ \}$ $\Delta = 0 : S=\{-\frac{b}{2a} \}$ $\Delta \gt 0$ : $S = \{\frac{-b+\sqrt \Delta}{2a} ; \frac{-b-\sqrt \Delta}{2a} \}$

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 $2x^2 - x - 6 = 0$ $\Delta = 49 \;\;\;\;\;\;\;\; S =\{ \frac{3}{2} ; 2\}$ $2x^2 - 3x +\frac{9}{0} = 0$ $\Delta = 0 \;\;\;\;\;\;\;\; S = \{ \frac{3}{4}\}$ $x^2 + 3x + 10 = 0$ $\Delta = -31 \;\;\;\;\;\;\;\; S =\{\} = \emptyset$