Solve a quadratic equation with the quadratic formula and display real or complex roots when supported.
Equation Solutions
How the Quadratic Formula Finds Roots
For an equation in the form ax² + bx + c = 0, the calculator evaluates the discriminant, b² − 4ac, and applies the quadratic formula. A positive discriminant produces two distinct real roots, zero produces one repeated real root, and a negative discriminant produces a complex-conjugate pair.
Check the equation form
Enter the coefficients for a, b, and c in the standard form. The leading coefficient a must not be zero; otherwise the equation is linear rather than quadratic. Results are rounded for display, so retain more precision when checking by substitution.
Example and limitations
For example, x² − 5x + 6 = 0 has roots 2 and 3. A negative discriminant produces complex roots; if the leading coefficient is zero, the expression is not a quadratic equation.