Manipulating expressions in the rootsEdexcel International A Level Further Maths: Mind map

Sum and product

Squares

Roots of quadratics

expressions in $\alpha$ and $\beta$

sumproductno solving

Cubes and fourth powers

Fractions

Using conditions

Exam questions on Manipulating expressions in the roots

The roots of the equation $x^2-6x+4=0$ are $\alpha$ and $\beta$ .
Find the value of $(\alpha+1)(\beta+1)$ .2 marks
The roots of the equation $2x^2+5x-3=0$ are $\alpha$ and $\beta$ .
Find the exact value of $(\alpha-\beta)^2$ .2 marks
The roots of the equation $x^2-5x+2=0$ are $\alpha$ and $\beta$ .
Find the value of $\alpha^3+\beta^3$ .3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).