Explanation

(a)
Let $\alpha$ be the root of equation $ax^{2} + bx + c = 0$ then $\frac{1}{\alpha}\$be a root of second equation, therefore
$a\alpha^{2} + b\alpha + c = 0$ ….(i)
and $a^{'}\frac{1}{\alpha^{2}}{+ \ b}^{'}\frac{1}{\alpha} + c^{'} = 0$
or $c^{'}\alpha^{2} + b^{'}\alpha + a^{'} = 0$ ...(ii)
On solving Eqs. (i) and (ii), we get
$\frac{\alpha^{2}}{ba^{'} - b^{'}c} = \frac{\alpha}{cc^{'} - aa'} = \frac{1}{ab^{'} - bc'}$
$\Rightarrow \left( cc^{'} - aa^{'} \right)^{2} = \left( ba^{'} - cb^{'} \right)(ab^{'} - bc^{'})$