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Guide

How to Solve a Quadratic Equation

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.

How to use the Quadratic Equation Solver

  1. Rewrite your equation as ax^2 + bx + c = 0.
  2. Enter the values of a, b and c.
  3. Read the discriminant and the roots.
  4. 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.

Try the Quadratic Equation Solver Free, instant, and runs in your browser.