You have aready seen several results for finding the values of expressions relating to the roots of a polynomial

⇒ In addition to these you have also used the following results for the roots of quadratic equations:

⇒ There are equivalent results to these for the roots of cubic and quartic equations

⇒ You can find an expression for the sum of the squares of a quartic equation in a similar way, by multiplying out (α + β + γ + δ)²

⇒ You can find a similar result for the sum of the cubes of a cubic equation y multiplying out (α + β + γ)³

⇒ Also see our notes on:

• Roots of a Quadratic Equation
• Roots of a Cubic Equation
• Roots of a Quartic Equation
• Linear Transformations of Roots