Quadratic Equation Solver
Roots, discriminant, vertex and the worked steps.
Quadratic Equation Solver finds the roots of ax² + bx + c = 0, including complex roots, and shows the discriminant, the vertex, the axis of symmetry and the factored form. It works through the quadratic formula step by step and plots the parabola in your browser, with no server involved.
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How to use Quadratic Equation Solver
- Enter the coefficients a, b and c.
- Read the roots, discriminant and vertex.
- Follow the worked steps or look at the plotted parabola.
Questions about Quadratic Equation Solver
What does the discriminant tell me?
b² − 4ac decides the shape of the answer. Positive gives two distinct real roots; zero gives one repeated root where the parabola just touches the axis; negative gives a conjugate pair of complex roots and a parabola that never crosses the axis.
Does it handle complex roots?
Yes, reported in the form p ± qi with the real and imaginary parts given exactly where possible.
What if a is zero?
Then it is not quadratic but linear, and the tool solves bx + c = 0 instead of dividing by zero — with a note explaining the switch.
Is the factored form exact?
It is exact when the roots are rational, and a decimal approximation to four places when they are not — the factors are built from the computed roots rather than from surd arithmetic. When the discriminant is negative there is no real factorisation, so that field is left out.
Can it solve cubics or simultaneous equations?
No. It handles second-degree equations in one variable, plus the linear case when a is zero. Cubics, quartics and systems of equations are outside what this page does, and it will not pretend otherwise by fitting them to the quadratic formula.
Is Quadratic Equation Solver really free, with no limits?
Yes. There is no account, no daily cap, no file-size tier and no watermark, because there is no server cost to recover. The site is funded by clearly disclosed partner recommendations on the Partners page, never by metering the tools.
Are my files or text uploaded when I use Quadratic Equation Solver?
No. Everything is processed by JavaScript running in your browser, on your device. You can verify it: open your browser's developer tools, switch to the Network tab, and use the tool. You will see no request carrying your data — because there is nowhere for it to go.