The quadratic formula solves equations in the form ax² + bx + c = 0. The discriminant tells you whether the equation has two, one or no real roots.
Identify the coefficients
Rewrite the equation in standard form and label the coefficient of x² as a, the coefficient of x as b and the constant as c. The a value cannot be zero for a quadratic equation.
Read the discriminant
The discriminant is b² − 4ac. A positive value gives two real roots, zero gives one repeated real root and a negative value gives no real roots in the real-number system.
Check the answer
Substitute each root back into the original equation when accuracy matters. Rounding can make a correct root appear slightly imperfect.
- Keep signs with the coefficients.
- Check that a is not zero.
- Use enough precision for the final step.
Frequently asked questions
What if the discriminant is negative?
There are no real roots. Complex-number methods are needed to express the solutions.
Can I use the formula when b is zero?
Yes. A zero coefficient is valid as long as a is not zero.