The original equation is 2x² − 5x − 3 = 0.

The original equation is $2x^2 - 5x - 3 = 0$.
Let the roots of this equation be $\alpha$ and $\beta$.
Using Vieta's formulas:
Sum of roots: $\alpha + \beta = -\frac{(-5)}{2} = \frac{5}{2}$
Product of roots: $\alpha \beta = \frac{-3}{2}$

The general form of a quadratic equation with roots $r_1$ and $r_2$ is $x^2 - (r_1 + r_2)x + r_1 r_2 = 0$. We will multiply by a common denominator to ensure integer coefficients.

*a) (i) Roots are $\frac{1}{\alpha