Answers by visitors named: Prahlad
We know for any quadratic polynomial f(x)=ax^2+bx+c with roots alpha(p) and beta(q)
(x-p)(x-q)= K[x^2-(p+q)x+pq]
So we express (p+q) as -b/a and pq as c/a.....
A.)(p^2/q) + (q^2/p)=?
By simply taking LCM, we can write the above statement as
(p^3+q^3)/pq
=(p+q)(p^2+q^2-pq)[identity used]
{Now what you must understand here is that we can only substitute the values of the sum and products of the roots- so our attempt now must be towards expressing this in the form of (p+q) or pq only}
=(p+q)((p+q)^2-3pq)
On reducing by substitution-
You will obtain (3abc-b^3)/a^3