Roots of Polynomials

• If α and β are roots of a quadratic equation then:

  • α + β = - b/a
  • α β = c/a
• If α, β and γ are roots of a cubic equation then:

  • α + β + γ = - b/a
  • α β + β γ + α γ = c/a
  • α β γ = - d/a
• If α, β, γ and δ are roots of a quartic equation, then:

  • α + β + γ + δ = - b/a
  • α β + α γ + α δ + β γ + β δ + γ δ = c/a
  • α β γ + α β δ + α γ δ + β γ δ = - d/a
  • α β γ δ = e/a
• The rules for reciprocals are:

  
• The rules for products of powers are:

  
• The rules for the sum of cubes are: