Given the sums and productsof the roots of polynomials, it is possible to find the equation of a second polynomial whose roots are a linear transformation of the first

⇒ For example, if the roots of a cubic equation are α, β, and γ, you need to be able to find the equation of a polynomial with roots (α + 2), (β + 2), and (γ + 2) or 3α, 3β, and 3γ

⇒ Also see our notes on:

• Roots of a Quadratic Equation
• Roots of a Cubic Equation
• Roots of a Quartic Equation
• Expressions Relating to the Roots of a Polynomial