Sum and product of rootsEdexcel International A Level Further Maths: Mind map

Exam questions on Sum and product of roots

1. The roots of the equation $2x^2-7x+4=0$ are $\alpha$ and $\beta$.
   Find the value of $\dfrac1\alpha+\dfrac1\beta$.2 marks
2. The roots of the equation $x^2+6x+7=0$ are $\alpha$ and $\beta$.
   Find a quadratic equation, with integer coefficients, whose roots are $2\alpha$ and $2\beta$.2 marks
3. The roots of the equation $3x^2-5x+1=0$ are $\alpha$ and $\beta$.
   Show that $\alpha^2+\beta^2=\frac{19}{9}$.3 marks