Math

Quadratic Formula Calculator

There are no real roots — the solutions are complex numbers.

Solve ax² + bx + c = 0 for its real roots.

Calculated Output

Root x₁ 2

Root x₂ 1

Discriminant 1

Formula: x = (−b ± √(b² − 4ac)) ÷ 2a

Step-by-Step Breakdown

1. Values used:

2. a = 1

3. b = -3

4. c = 2

6. Root x₁ = 2

7. Root x₂ = 1

8. Discriminant = 1

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The math behind it

x = (−b ± √(b² − 4ac)) ÷ 2a. The discriminant b² − 4ac tells you the number of real roots: >0 gives two, =0 gives one, <0 gives none (complex).

x² − 3x + 2 = 0 → disc = 1, roots x = 2 and x = 1.

What if the discriminant is negative?

There are no real roots — the solutions are complex numbers.