Solving the Quadratic Equation

A quadratic equation is a polynomial equation of the second degree, having the general form:

$a x^{2} + b x + c = 0$

The letters a, b and c are called coefficients: a is the coefficient of x², b is the coefficient of x, and c is the constant coefficient. A quadratic equation has two complex roots (i.e., solutions for the unknown term x). In some cases, these roots can have the same value. The roots can also belong to the realm of complex numbers. The values of the roots can be computed using the quadratic formula as shown below:

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

For example, the roots of the quadratic equation

$2 x^{2} - 14 x + 20 = 0$

can be determined by first substituting 2 for a, -14 for b, and 20 for c

$x = \frac{14 \pm \sqrt{{(-14)}^{2} - 4 (2) (20)}}{2 (2)}$

and then solving the expression, which gives the roots of the equation as either x = 5 or x = 2.

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