1.6: Transform the roots of a quadratic

(a) Show that

The quadratic equation

where $\displaystyle k$ is a positive constant, has roots $\displaystyle \alpha$ and $\displaystyle \beta$, where $\displaystyle \alpha>\beta$.

(b) Show that

(c) Hence form a quadratic equation with roots $\displaystyle \alpha+1$ and $\displaystyle \beta-1$. Give your equation in the form

where $\displaystyle p$ and $\displaystyle q$ should be given in terms of $\displaystyle k$.