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  • A-Level Further Maths

Roots of Polynomials

Won't lie, this topic isn't particularly fun. It's just a whole lot of algebra and equations that you need to know and get right. At least the topic is small.


To be perfectly honest, the only challenge is writing everything out clearly, and not getting confused between the Greek and Latin alphabets:

  • don't confuse a with α

  • don't confuse b with β

  • don't confuse g with γ

  • don't confuse d with δ

a, b, c, d & e are real constants
α, β, γ, δ are roots of polynomials


Quadratic Polynomials

A quadratic equation in the form ax² + bx + c = 0 has two possible roots, α and β. These can be distinct and real, repeated (the same), or complex conjugates.


The roots can be added or multiplied to give the following results:

Roots of polynomials equations. Free online a-level further maths core pure 1 CP1 notes. EngineeringNotes.net, EngineeringNotes, Engineering Notes.

Squaring or cubing the roots gives different results:

Roots of polynomials equations. Free online a-level further maths core pure 1 CP1 notes. EngineeringNotes.net, EngineeringNotes, Engineering Notes.



Cubic Polynomials

A cubic equation in the form ax³ + bx² + cx + d = 0 has three possible roots, α, β and γ.