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

Based on the value of the discriminant, roots can be divided to 3 types : ^[1]

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

${\displaystyle x=-b/(2a)}$

• if Δ<0, two complex roots

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

The sum of the roots is equal to ${\displaystyle -b/a}$

The product of the roots is equal to ${\displaystyle c/a}$ ^[2]