Quadratic Equation Calculator
Solve ax² + bx + c = 0, including repeated, complex and linear cases.
Your result
MATHEnter your values and select calculate.
On this page How it works & practical examples
How to use the Quadratic Equation Calculator
Enter the three coefficients after moving every term to the left-hand side. The discriminant determines whether a true quadratic has two distinct real roots, one repeated root or a pair of complex roots. If a is zero, the calculator handles the remaining linear equation rather than dividing by zero. If both a and b are zero, it reports whether the constant equation has no solution or holds for every real number.
The calculation
Worked example
For x² − 3x + 2 = 0, the discriminant is 1 and the roots are 1 and 2. For x² + 1 = 0, the roots are ±i.
Assumptions and limits
The calculation uses floating-point arithmetic and a stable rearrangement for real roots to reduce cancellation. Very small coefficients or nearly repeated roots can still be sensitive to measurement and rounding. Complex results are displayed as real part plus or minus an imaginary component. This is a numerical root calculator rather than symbolic algebra.
Common questions
What if a is zero?
The equation becomes linear when b is non-zero. If a and b are both zero, c determines whether there are no solutions or infinitely many.
Does a negative discriminant mean no solution?
It means no real roots. Complex roots still exist and are displayed using i, whose square is −1.