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LearnEdexcel9FM0First teaching 2017Paper 2 · Core Pure Mathematics 2Further algebra and functions

Paper 2 · Module

Further algebra and functions

2 subtopics≈ 80 min in total

Start the module: Roots of polynomial equations Open graphing calculator

Roots of polynomial equations
For $ax^2+bx+c=0$ : $\alpha+\beta=-\frac ba$ , $\alpha\beta=\frac ca$ . Cubics and quartics have similar sums of roots taken one, two, three at a time. These let you evaluate expressions in the roots, and build new equations, without solving.
≈ 40 min
Summation of series
$\sum r=\frac12n(n+1)$ , $\sum r^2=\frac16n(n+1)(2n+1)$ , $\sum r^3=\frac14n^2(n+1)^2$ . Combine them for polynomial sums. When each term is a difference $f(r)-f(r+1)$ , almost everything cancels: the method of differences.
≈ 40 min