Quadratic Formula Calculator
A quadratic equation has an x squared term. Enter the three numbers a, b and c, and this finds the roots, the values of x that make the equation equal zero.
- Free
- Works offline after your first visit
- Saves on this device
- No sign-up
- Updated
How it works
The discriminant is b squared minus four times a times c. It shows the kind of roots: two real roots if it is positive, one repeated root if it is zero, and no real roots if it is negative.
The roots are negative b, plus or minus the square root of the discriminant, all divided by two times a. When there are no real roots, the roots show as zero and the kind line says so.
Worked example
With a of 1, b of -3 and c of 2, the kind of roots is two real roots. The first root is 2, and the second is 1.
Questions
What if a is zero?
Then the equation is not quadratic, and the formula divides by zero. Enter a number other than zero for a.
What does the discriminant mean?
It is the part under the square root. Its sign tells you whether the roots are real numbers.
Why do some roots show zero?
When the discriminant is negative, the roots are not real numbers, so the calculator shows zero. The kind line tells you there are no real roots.
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