Calculator guide
Solve a quadratic equation ax²+bx+c=0 and inspect its real or complex roots.
Formula or method
x = (−b ± √(b²−4ac))/(2a); the discriminant D=b²−4ac determines the root type.
How to use this calculator
- Enter coefficients a, b, and c.
- Confirm a is not zero.
- Review both roots and the discriminant.
Worked example
For x²−5x+6=0, D=25−24=1 and roots are (5±1)/2, or x=3 and x=2.
Understanding the result
D>0 gives two real roots, D=0 one repeated real root, and D<0 a complex-conjugate pair.
Limitations and assumptions
- This tool solves the equation represented by the entered coefficients only.
- Very large or nearly equal coefficients can introduce floating-point rounding.
Frequently asked questions
What if a is zero?
The equation becomes linear and is not quadratic.
What does a negative discriminant mean?
There are no real x-intercepts, but complex roots still exist.
How can I check a root?
Substitute it into ax²+bx+c; the result should be near zero.
Sources
Educational information only; verify important decisions with a qualified professional.