Last updated on Sep 20, 2026

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

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Roots of Polynomials

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What are the roots of a polynomial $f(x)$ ?

Values that satisfy $f(x) = 0$

For polynomial $a_nx^n + a_{n-1}x^{n-1} + \dots + a_0 = 0$ , what is the sum of roots $S_1$ ?

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

For polynomial degree $n$ , what is the product of all roots $P = \alpha\beta\gamma\dots$ ?

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

For cubic $ax^3 + bx^2 + cx + d = 0$ with roots $\alpha, \beta, \gamma$ , find $\alpha + \beta + \gamma$ .

$-\frac{b}{a}$

For cubic $ax^3 + bx^2 + cx + d = 0$ , what is $\alpha\beta\gamma$ ?

$-\frac{d}{a}$

For cubic $ax^3 + bx^2 + cx + d = 0$ , what is $\alpha\beta + \beta\gamma + \gamma\alpha$ ?

$\frac{c}{a}$

What is $\alpha^2 + \beta^2 + \gamma^2$ in terms of $S_1$ and $S_2$ ?

$S_1^2 - 2S_2$

For cubic $ax^3 + bx^2 + cx + d = 0$ , what is $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma}$ ?

$-\frac{c}{d}$

What is the expansion of $(c + \alpha)(c + \beta)(c + \gamma)$ using $S_1, S_2, P$ ?

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

A common mistake is confusing $S_2$ with what?

$P$ (product of all roots)

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Roots of Polynomials

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Maclaurin Series

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Roots of Polynomials

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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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