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

Exam questions on Forming quadratic equations with new roots

1. 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
2. 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
3. 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