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Quadratic Formula

In the real number system, a positive real number b has two square roots, √b and -√b, and negative real numbers have no square roots. In the complex number system, a negative real number -b has two imaginary square roots, i√b and -i√b. The quadratic formula gives the roots of any second degree polynomial in the complex number system.

The roots of the polynomial

az2 + bz + c

where a ≠ 0 in, the complex number system are given by

14_differential_equations-123.gif

The number b2 - 4ac is called the discriminant. If a, b, and c are real, there are three cases:

Case 1

If b2 - 4ac > 0, there are two real roots.

Case 2

If b2 - 4ac = 0, there is one real root.

Case 3

If b2 - 4ac < 0, there are two complex roots, which are complex conjugates of each other.

Home Differential Equations Complex Numbers Quadratic Formula

Last Update: 2006-11-16