Consider a quadratic equation of the form:
This is treated as an equation in . The quadratic formula is a formula to determine the solutions of this equation. The short version of the formula is that the roots are:
if the expression makes sens; otherwise there are no roots.
To understand the formula, first define the discriminant of the quadratic function as the value . Now, we make three cases:
|Case for discriminant||Conclusion for roots||Conclusion for factorization of polynomial|
|positive, i.e.,||there are two real roots, given as and||If we denote the roots by , then|
|zero, i.e.,||there is a single real root with multiplicity two, and that root is|
|negative, i.e.,||there are no real roots||the polynomial does not factor, i.e., it is irreducible|