Edexcel A-Level Mathematics AS Fp1 2 2 Manipulation of Expressions Questions

Practise Edexcel IAL FP1.2.2 by rewriting powers of quadratic roots in terms of α+β and αβ, then simplifying exact answers.

Exam points

calculate α²+β² from (α+β)²-2αβ before substituting fractions or parameters
calculate α³+β³ from (α+β)³-3αβ(α+β) before substituting fractions or parameters

[Maximum number: 2]

The quadratic equation

2 x^{2}-3 x+7=0

has roots $\alpha$ and $\beta$
Without solving the equation,

determine the value of $\alpha^{2}+\beta^{2}$

$\alpha^{2}+\beta^{2}=(\alpha+\beta)^{2}-2 \alpha \beta$ $=\left(\frac{3}{2}\right)^{2}-2\left(\frac{7}{2}\right)=-\frac{19}{4}$
(2)

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