Rules. Quadratic equation and its solution.
A quadratic equation is a polynomial equation of the second degree. The general form is
a x
^{2} + b x
+ c
= 0,a
≠ 0.
Solve quadratic equation means to find all the values
x_{i}
, in which will be the equality
a x_{i}
^{2} + b x_{i}
+ c
= 0. ∆ =
b
^{2}  4 a c
. If the discriminant is positive (∆ > 0), then there are two distinct roots, both of which are real numbers.
 If the discriminant is zero (∆ = 0), then there is exactly one distinct real root, sometimes called a double root (x_{1} =x_{2}).
 If the discriminant is negative (∆ < 0), then there are no real roots.
The roots are given by the quadratic formula

Vieta theorem
For the mentioned quadratic equation
x
^{2} + px
+ q
= 0p
which is drawn with the opposite sign and root’s product is equal to free term q
:
x
_{1} + x
_{2} = p
;x
_{1}x
_{2} = q
.