📐 Quadratic equation solver
Solve ax² + bx + c = 0 with the quadratic formula, step by step: the discriminant, the roots and the vertex.
1x² − 5x + 6 = 0
Discriminant: b² − 4ac = 25 − 24 = 1
x₁ = 3, x₂ = 2
Vertex: (2.5, -0.25), a minimum
Formula: x = (−b ± √(b² − 4ac)) / 2a
Questions and answers
Frequently asked questions
What is the quadratic formula?
x = (−b ± √(b² − 4ac)) / 2a. The part under the square root, b² − 4ac, is called the discriminant.
What does the discriminant tell me?
If it is positive there are two real roots, if it is zero there is one (a double root), and if it is negative there are no real roots, only two complex ones.
What is the vertex?
The turning point of the parabola, at x = −b/2a. It is a minimum when a is positive and a maximum when a is negative.
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