Calculator Inputs
a ≠ 0
Results
1.0000
Discriminant (b²−4ac)
Two distinct real roots
Nature
2.0000, 1.0000
Roots
About This Calculator
A quadratic equation has the form ax² + bx + c = 0. The quadratic formula finds its roots:
x = (−b ± √(b² − 4ac)) ÷ (2a)
Reading the Discriminant
- b²−4ac > 0: two real roots
- = 0: one repeated root
- < 0: two complex (imaginary) roots
Frequently Asked Questions
What if a = 0?
Then it is not quadratic — it becomes a linear equation bx + c = 0, solved as x = −c/b. This calculator requires a ≠ 0.
What does a negative discriminant mean?
It means the parabola never crosses the x-axis, so there are no real solutions — only complex ones involving the imaginary unit i.