User:AH-2031/Quadratic formula

The discriminant Δ of the quadratic equation is equal to $$b^2 - 4ac $$

Based on the value of the discriminant, roots can be divided to 3 types :


 * if Δ>0, two real distinct roots$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\ \ $$
 * if Δ=0, one double root

$$x=- b / (2a) $$


 * if Δ<0, two complex roots


 * $$x = \frac{-b \pm i \sqrt{b^2 - 4ac}}{2a}\ \ $$

The sum of the roots is equal to $$-b/a$$

The product of the roots is equal to $$c/a $$