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Add section on discriminant and nature of solutions
x = 2\mathrm{i}, \, x=-2\mathrm{i}
x = 2\mathrm{i}, \, x=-2\mathrm{i}
</math>
</math>
==The discriminant and nature of solutions==
In general, the ''a, b'' and ''c'' coefficients can be [[complex number]]s. The solutions are then also complex numbers. However, if the ''a, b'' and ''c'' coefficients are restricted to being [[real number]]s then the possible solutions fall into three categories described by the discriminant. The discriminant is the part inside the square root of the quadratic formula, namely,<ref name=britannica/>
:<math>
b^2 - 4ac
</math>
The value of the discriminant can either be greater than zero, equal to zero or less than zero:
*If it is greater than zero, the quadratic has two real solutions.
*If it is zero, the quadratic has only one real solution. The solution is sometimes called a repeated root.
*If it is less than zero, the square root evaluates to an [[imaginary number]]. There are then two complex solutions which are [[complex conjugate]] of each other.
== References ==
== References ==