# Summary and Main Ideas

## Summary

• 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 rootsIrrational roots $$\Delta > 0$$$$Δ =$$ squared rational number$$Δ =$$ not squared rational number