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• Zero product law: if $$a \times b = 0$$, then $$a = 0$$ and/or $$b=0$$.
• Quadratic formula: $$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$.
• Discriminant: $$\Delta = b^2 - 4ac$$.
 Nature of roots Discriminant Roots are non-real $$\Delta <0$$ Roots are real and equal $$\Delta = 0$$ Roots are real and unequal: Rational roots Irrational roots $$\Delta > 0$$ $$Δ =$$ squared rational number $$Δ =$$ not squared rational number