Last updated on Nov 05, 2026

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

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Roots of Polynomials

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Roots of polynomial

Values that satisfy $f(x) = 0$

Sum of roots $S_1$ for degree $n$ poly

$S_1 = -\frac{a_{n-1}}{a_n}$

Sum of products (2 roots) $S_2$ for degree $n$

$S_2 = \frac{a_{n-2}}{a_n}$

Product of all roots $P$ for degree $n$

$P = (-1)^n \frac{a_0}{a_n}$

$\alpha + \beta + \gamma$ for $ax^3+bx^2+cx+d=0$

$-\frac{b}{a}$

$\alpha\beta + \beta\gamma + \gamma\alpha$ for cubic

$\frac{c}{a}$

$\alpha\beta\gamma$ for $ax^3+bx^2+cx+d=0$

$-\frac{d}{a}$

$\alpha^2 + \beta^2 + \gamma^2$ in terms of $S_1, S_2$

$S_1^2 - 2S_2$

$\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma}$ formula

$\frac{S_2}{P}$

$(c+\alpha)(c+\beta)(c+\gamma)$ expanded

$c^3 + S_1c^2 + S_2c + P$

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Roots of Polynomials

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Maclaurin Series

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Roots of Polynomials

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Maclaurin Series

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Roots of Polynomials

Series

Maclaurin Series

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Roots of Polynomials

Series

Maclaurin Series

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