A quadratic polynomial is a polynomial of polynomial degree 2. A univariate polynomial of
this polynomial degree has the form 
with 
. An equation involving a
quadratic polynomial is called a quadratic equation.
A closed-form solution known as the quadratic formula
exists for the solutions of an arbitrary quadratic
equation.
For the monic polynomial 
with real coefficients,
the polynomial discriminant is 
. There is at least one real
root iff 
, and two distinct real
roots iff 
. If both roots are real,
then the coefficients satisfy the sharp inequality
 |
where 
denotes the maximum. Equality holds iff 
or 
, corresponding to 
and 
, respectively. Thus the constant 
cannot be decreased (Moser and Pounder 1962; Dixon 1962,
p. 259; Trott 2006).
