To solve ax squared plus bx plus c equals 0, enter a, b and c into the Quadratic Equation Solver. It shows the discriminant and both real roots, using the quadratic formula x = (-b plus or minus the square root of b squared minus 4ac) divided by 2a.
Follow along with the free Quadratic Equation Solver, which runs in your browser, or browse more tools in this category.
How to use the Quadratic Equation Solver
- Rewrite your equation as ax^2 + bx + c = 0.
- Enter the values of a, b and c.
- Read the discriminant and the roots.
- Substitute a root back into the equation to check it.
Worked example
For x^2 – 5x + 6 = 0, a is 1, b is -5 and c is 6. The discriminant is 25 – 24 = 1, so the roots are x = 2 and x = 3.
Tips and common mistakes
- If the discriminant is negative there are no real roots.
- If it is zero there is exactly one repeated root.
- The value of a cannot be zero, otherwise the equation is not quadratic.
Frequently asked questions
What is the discriminant?
The value b squared minus 4ac. It tells you how many real roots exist.
What if there are no real roots?
The tool reports that the equation has no real solutions.
Can a be zero?
No, then it would be a linear equation.