How to Solve a Quadratic Equation With the Quadratic Formula
Every quadratic equation can be solved with one formula. This guide explains the discriminant and works through an example.
What is the Quadratic Equation Calculator?
Enter the three coefficients a, b and c. The tool first works out the discriminant, b squared minus 4ac, which tells you whether real roots exist. When the discriminant is zero or positive, it applies the quadratic formula, negative b plus or minus the square root of the discriminant, all divided by twice a.
How to use it
- Enter a, the coefficient of x squared.
- Enter b and c.
- Calculate to see the discriminant and the roots.
Worked example
x squared - 3x + 2 = 0 has discriminant 1 and roots 2 and 1.
What are the roots of x squared minus 3x plus 2 equals zero?
Here a is 1, b is negative 3 and c is 2, so the discriminant is 9 minus 8, which is 1. Applying the formula gives roots of 2 and 1. You can check them: both values make the equation equal zero.
Frequently asked questions
What if a is zero?
Then the equation is not quadratic at all, it is a straight-line equation, so the tool says so instead of giving quadratic roots.
What does a negative discriminant mean?
It means there are no real roots, because you cannot take the square root of a negative number in ordinary real arithmetic.