Every polynomial equation has at least one root, real or imaginary ( complex).
Every polynomial equation of degree has exactly roots real or imaginary.
A quadratic equation cannot have more than two roots.
If is the quadratic equation we get, the roots
If , then and the roots are
If but is not a perfect square, then the roots are irrational and unequal.
If then the roots are imaginary and are give by
Complex roots of an equation with real coefficient always occur in pairs. However, this may not be true in case of the equations with complex coefficient. For example, has both roots equal to .
Surd root of an equation with rational coefficient always occurs in pairs like and . However, Surd roots of an equation with irrational coefficients may not occur in pairs. For example, has both roots equal to .