The quadratic equation calculator accepts the coefficients a, b, and c of a quadratic equation in the standard form, and then calculates the roots of the equation, including complex roots. The formulas can be found below the calculator.

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Created: 2011-07-23 20:16:59, Last updated: 2023-04-04 03:19:14

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For example, given the quadratic equation $2x^2 + 5x - 3 = 0$, the calculator would find the roots x = 0.5 and x = -3. If given the quadratic equation $x^2 + 2x + 5 = 0$, the calculator would find the roots in complex form as x = -1 + 2i and x = -1 - 2i, where i represents the imaginary unit.

Digits after the decimal point: 2
x1

x2

A quadratic equation is a second-order polynomial equation in a single variable x
$ax^2+bx+c=0$
where a != 0

The calculator uses the standard quadratic formula,
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

There are three cases:

If the discriminant $b^2-4ac$
is positive, the equation has two real roots

if the discriminant $b^2-4ac$
is zero, there is one real root

if the discriminant $b^2-4ac$
is negative, there are two complex roots.

The calculator displays the roots in either real or complex form, depending on the values of the coefficients.

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

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

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