수학

이차방정식 풀이기

근의 공식으로 단계별로 이차방정식 풀기

ax² + bx + c = 0
x²
+
x
+
사용 방법
  1. Enter coefficients a, b, and c for the equation ax² + bx + c = 0.
  2. Results — roots, discriminant, and vertex — appear instantly as you type.
  3. Use the preset buttons to try common equations.
  4. If Δ < 0, complex (imaginary) roots are shown in the form p ± qi.

공식

Quadratic Formula:

x = (−b ± √(b² − 4ac)) / 2a

The Discriminant (Δ = b² − 4ac) determines the nature of roots:

  • Δ > 0 → Two distinct real roots
  • Δ = 0 → One real root (repeated)
  • Δ < 0 → Two complex conjugate roots

Vertex of parabola: (h, k) where h = −b/2a, k = c − b²/4a