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How to solve a quadratic equation
Provide the three coefficients and interpret the discriminant and roots.
Enter coefficients
Enter non-zero a and any finite values for b and c.
Calculate the discriminant
The calculator evaluates b² − 4ac to determine the root type.
Interpret the roots
Review the real or complex roots and the parabola vertex.
Frequently Asked Questions
What is the standard quadratic form?
A quadratic equation is written as ax² + bx + c = 0 with a not equal to zero.
What does the discriminant show?
It identifies whether there are two real roots, one repeated real root, or complex roots.
Why can a not be zero?
When a is zero, the x² term disappears and the equation is no longer quadratic.
What are complex roots?
Complex roots contain the imaginary unit i and occur when the discriminant is negative.
What is the vertex?
The vertex is the turning point of the parabola represented by the quadratic.
Can coefficients be decimals?
Yes. Any finite numeric coefficients are accepted.
How are roots rounded?
Results are formatted for readability while calculations use JavaScript number precision.