Quadratic Formula Calculator
Enter the coefficients of ax² + bx + c = 0 to get the discriminant and the real or complex roots.
Type the coefficients a, b, and c of the quadratic equation ax² + bx + c = 0. The calculator evaluates the discriminant (D) and applies the quadratic formula to return the roots to full decimal precision, whether they're real or complex.
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How to use
- Enter the three coefficients a, b, and c in order (a cannot be zero).
- As you type, the sign of the discriminant D = b² − 4ac is analyzed to tell you whether the roots are two real, one repeated, or complex.
- Review the worked substitution into the quadratic formula and the final roots (including complex form), then copy them.
FAQ
- What happens when the discriminant D is negative?
- A negative discriminant means there are no real roots. The calculator then uses the imaginary unit i to return two distinct complex roots in the form (real part ± imaginary part i).
- Why won't the calculator work if I enter 0 for coefficient a?
- By definition, a quadratic equation requires a nonzero coefficient a on the x² term. If a is 0, the squared term disappears and the equation becomes linear (bx + c = 0), so the quadratic formula and discriminant no longer apply. In that case, the calculator lets you know the input no longer meets the conditions for a quadratic equation.
- Why won't the calculator work if I enter 0 for coefficient a?
- By definition, a quadratic equation requires a nonzero coefficient a on the x² term. If a is 0, the squared term disappears and the equation becomes linear (bx + c = 0), so the quadratic formula and discriminant no longer apply. In that case, the calculator lets you know the input no longer meets the conditions for a quadratic equation.