Quadratic Equation Solver
Enter the three coefficients of a quadratic equation to evaluate its discriminant, roots and vertex.
Discriminant1
Root 13
Root 22
Vertex(2.5, -0.25)
How this tool works
Discriminant D = b²−4ac. Roots are (−b ± √D)/(2a); negative D produces a complex-conjugate pair.
Example
For x²−5x+6=0, the roots are 2 and 3 and the discriminant is 1.
Common questions
What if a equals zero?
Then the expression is not quadratic; if b is nonzero the tool returns the corresponding linear root.
What does a negative discriminant mean?
The equation has no real roots and instead has two complex conjugate roots.