Forming quadratic equations with new rootsEdexcel International A Level Further Maths: Flashcards

What these 12 flashcards ask

Quadratic with roots p and q?
New equation with roots \frac1\alpha,\frac1\beta: sum of new roots?
New equation with roots \frac1\alpha,\frac1\beta: product of new roots?
Shortcut for the equation with roots \frac1\alpha,\frac1\beta of ax^2+bx+c=0?
Sum and product of the new roots \alpha^3,\beta^3?
Sum and product of the new roots \alpha^2,\beta^2?
Sum of the new roots \frac{1}{2\alpha},\frac{1}{2\beta}?
Product of the new roots \frac{1}{2\alpha},\frac{1}{2\beta}?
Sum of the new roots \alpha+\frac2\beta,\ \beta+\frac2\alpha?
Product of the new roots \alpha+\frac2\beta,\ \beta+\frac2\alpha?
How do you get integer coefficients?
Do you need to solve the original quadratic?

Exam questions on Forming quadratic equations with new roots

The roots of the equation $2x^2-7x+3=0$ are $\alpha$ and $\beta$ .
Find an equation, with integer coefficients, that has roots $\alpha+1$ and $\beta+1$ .2 marks
The roots of the equation $x^2-4x+2=0$ are $\alpha$ and $\beta$ .
Find an equation, with integer coefficients, that has roots $\frac1\alpha$ and $\frac1\beta$ .2 marks
The roots of the equation $x^2-5x+2=0$ are $\alpha$ and $\beta$ .
Find an equation, with integer coefficients, that has roots $\frac{1}{2\alpha}$ and $\frac{1}{2\beta}$ .3 marks

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).