Linear Transformations of Roots (Edexcel A-Level Further Mathematics): Flashcards

A polynomial whose roots are related to original roots by $y = p\alpha + q$

$y = p\alpha + q$ where $p$, $q$ are constants

Express $\alpha$ (original root) in terms of $y$

$\alpha = \frac{y - q}{p}$

Substitute $\alpha = \frac{y-q}{p}$ into original polynomial

Clear fractions by multiplying through by $p^n$

$p^n$ where $n$ is degree of original polynomial

Ensure $\alpha$ correctly expressed as $\frac{y-q}{p}$ from $y = p\alpha + q$

Binomial powers like $(y - q)^n$ and $(y + q)^n$

Not multiplying all terms by appropriate power of $p$