Roots Of Polyomials

• Roots Of Quadratic

  • alpha + beta = -b/a
  • alpha*beta = c/a
• Roots Of A Cubic

  • alpha + beta + gamma = -b/a
  • (alpha*beta) + (beta*gamma) + (gamma*alpha) = c/a
  • alpha*beta*gamma = -d/a
• Abbreviations

  $\sum\alpha =$$-b/a$

  $\sum\alpha\beta =$$c/a$

  $\sum\alpha\beta\gamma =$$-d/a$
• Sum Of Squares


  $\sum\alpha^2 =$$(\sum\alpha)^2 - 2(\sum\alpha\beta)$
• Sum Of Cubes


  $\sum\alpha^2 =$$(\sum\alpha)^3 - 3\sum\alpha\beta\sum\alpha +$$3\alpha\beta\gamma$
• Transformations Of Roots


  If roots are a(alpha) + b, set w = ax + b

  Rearrange for x and substitute in
• Parametric (x-axis)


  $\pi\int y^2 dx/dt dt$
• Parametric (y-axis)


  $\pi\int x^2 dy/dt dt$