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Quadratic Equation Solver

Solve any quadratic equation of the form ax² + bx + c = 0. Enter the three coefficients to find all roots, the discriminant, vertex, and factored form.

Enter Coefficients (ax² + bx + c = 0)
a (x²)1
a
b (x)-5
b
c (constant)6
c
Discriminant (b²-4ac)
Root 1 (x₁)
Root 2 (x₂)
Vertex (h, k)
Axis of Symmetry
Factored Form
Frequently Asked Questions
What is a quadratic equation?

An equation of the form ax² + bx + c = 0 where a ≠ 0. It always has two solutions.

What is the quadratic formula?

x = (-b ± √(b²-4ac)) / 2a. Substitute a, b, c to get two solutions.

What is the discriminant?

b²-4ac. Positive: two real roots. Zero: one repeated root. Negative: two complex roots.

How do I solve x² - 5x + 6 = 0?

a=1, b=-5, c=6. Discriminant=1. x = (5±1)/2. Solutions: x=3 and x=2.

Where are quadratic equations used?

Projectile motion, profit optimisation, area calculations, and engineering stress analysis.