2.10 Summary

2.10 Summary (EMBFZ)

• 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