Part of ALG-05 — Quadratic Equations

Relation Between Roots and Coefficients for Cubics

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For ax3ax^3 + bx2bx^2 + cx + d = 0 with roots alpha, beta, gamma:

  • alpha + beta + gamma = -b/a
  • alphabeta + betagamma + gamma*alpha = ca\frac{c}{a}
  • alphabetagamma = -d/a

This extends Vieta's formulas. In JEE, cubic equations often appear in combination with quadratic theory — e.g., "one root is 1, find the quadratic formed by the other two."

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