The equation becomes linear bx + c = 0.

Can it return complex roots?

Yes. Negative discriminants are shown as a real part plus or minus an imaginary part.

What is the discriminant?

It is b² − 4ac, the value that determines the number and type of quadratic roots.

A discriminant of zero produces one repeated solution with multiplicity two.

The symbol i is the imaginary unit, defined by i² = −1.

Solve linear and quadratic equations, including repeated, complex, identity and no-solution cases.

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When a is zero, the solver automatically handles the equation as linear. A negative discriminant produces a complex conjugate pair.

Quadratic formulax = (−b ± √(b² − 4ac)) ÷ 2a

For x² − 5x + 6 = 0, the discriminant is 1 and the roots are 3 and 2.