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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

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:

Squaring or cubing the roots gives different results:

## Cubic Polynomials

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