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The solution of a quadratic equation

The solution of quadratic equation, including complex roots

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Timur

Timur

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
ax^2+bx+c=0
with a != 0

The roots x can be found using the quadratic formula
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

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
b^2-4ac
is called the discriminant of the quadratic equation

Using roots, polynomial equation can be expressed as
ax^2+bx+c=a(x-x_1)(x-x_2)

Below the calculator

PLANETCALC, Solution of quadratic equation

Solution of quadratic equation

Digits after the decimal point: 2
x1
 
x2
 

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