The solution of a quadratic equation

The solution of quadratic equation, including complex roots

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Created: 2011-07-23 20:16:59, Last updated: 2021-03-12 16:49:46
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A quadratic equation is a second-order polynomial equation in a single variable x
with a != 0

The roots x can be found using the quadratic formula

There are three cases:

if b^2-4ac>0
then there are two distinct roots, both of which are real numbers

if b^2-4ac=0
then there is exactly one distinct real root, sometimes called a double root

if b^2-4ac<0
then there are no real roots. Rather, there are two distinct (non-real) complex roots.

The expression
is called the discriminant of the quadratic equation

Using roots, polynomial equation can be expressed as

Below the calculator

PLANETCALC, Solution of quadratic equation

Solution of quadratic equation

Digits after the decimal point: 2

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PLANETCALC, The solution of a quadratic equation