Problem

The quadratic equation

$2x^2 – 3x + 7 = 0$

has roots $\alpha$ and $\beta$

Without solving the equation,

(a) write down the value of $(\alpha + \beta)$ and the value of $\alpha\beta$

(b) determine the value of $\alpha^2 + \beta^2$

(c) find a quadratic equation which has roots

$\left(\alpha - \frac{1}{\beta}\right) \text{ and } \left(\beta - \frac{1}{\alpha}\right)$

giving your answer in the form $px^2 + qx + r = 0$ where $p$, $q$ and $r$ are integers to be determined.