LEGACY Roots of Polynomials

A-Level Further Core 1

Sum and Product of Roots

Quadratic

Cubic

Quartic

How to remember

A good way to remember is that the sum of increasing amount of roots is equal to the next coefficient over with alternating sign (it goes and ):

• For Individual:
• For Pairs:
• For Triplets:
• For Quadruplets:

Reciprocals of Roots

Quadratic: Cubic: Quartic:

Sum of squares

Quadratic: Cubic: Quartic:

Sum of cubes

Quadratic: Cubic:

Linear Transformations of Roots

Given a polynomial in terms of with roots , you can find the polynomial in terms of with roots , , by using the equation , then rearranging for and plugging into the original polynomial and expanding and simplifying.

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