Problem

The quadratic equation

$Ax^2 + 5x - 12 = 0$

where $A$ is a constant, has roots $\alpha$ and $\beta$

(a) Write down an expression in terms of $A$ for

(i) $\alpha + \beta$

(ii) $\alpha\beta$

The equation

$4x^2 - 5x + B = 0$

where $B$ is a constant, has roots $\alpha - \dfrac{3}{\beta}$ and $\beta - \dfrac{3}{\alpha}$

(b) Determine the value of $A$

(c) Determine the value of $B$