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A second-order equation \( Ar + Bs + Ct + \cdots = 0 \) is classified by the sign of

  • A.\( A^{2} - 4BC \)
  • B.\( AC - B^{2} \)
  • C.\( B^{2} - 4AC \)
  • D.\( B^{2} + 4AC \)

Answer: C

The discriminant \( B^{2} - 4AC \) decides the type, exactly as it does for a conic: negative gives elliptic, zero parabolic and positive hyperbolic. The classification governs what kind of data the problem needs and how disturbances travel, so it is settled before any method of solution is chosen

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