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Quadratic Equation Solver

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.

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.

PLANETCALC, Solution of quadratic equation

Solution of quadratic equation

Digits after the decimal point: 2
x1
 
x2
 

Quadratic Equation Solution

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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