Quadratic formula

• A quadratic equation is an equation of the form $a{x}^2+bx+c=0$ (where $a\ne 0$)
• Its solutions are given by the quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
• The discriminant of this quadratic equation is $D=b^2-4ac$
  1. If $D>0$, then the equation has two distinct real solutions.
  2. If $D=0$, then the equation has exactly one real solution.
  3. If $D<0$, then the equation has no real solution.