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.
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For example, given the quadratic equation , the calculator would find the roots x = 0.5 and x = -3. If given the quadratic equation
, the calculator would find the roots in complex form as x = -1 + 2i and x = -1 - 2i, where i represents the imaginary unit.
Solution of quadratic equation
Quadratic Equation Solution
A quadratic equation is a second-order polynomial equation in a single variable x
where a != 0
The calculator uses the standard quadratic formula,
There are three cases:
If the discriminant
is positive, the equation has two real roots
if the discriminant
is zero, there is one real root
if the discriminant
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
is called the discriminant of the quadratic equation
Using roots, the quadratic equation can be expressed as
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