Roots of Polynomial Equations

Question 1

Quadratics: What does α + β = ?

Answer 1

-b/a

Question 2

Quadratics: What does αβ = ?

Answer 2

c/a

Question 3

What’s a symmetric function?

Answer 3

A function where α β and γ can be swapped without changing the function

Question 4

Quadratics: How do you find an equation with roots 2α and 2β, from an equation with roots α and β?

Answer 4

Let u be a new root
Workout α in terms of u
Sub u into equation given
Expand and simplify

Question 5

Cubics: What does α + β + γ = ?

Answer 5

-b/a

Question 6

Cubics: What does αβγ = ?

Answer 6

-d/a

Question 7

Cubics: βγ + αγ + αβ = ?

Answer 7

c/a

Question 8

How do you get rid of a +-√?

Answer 8

Put on one side of the

Square both sides