If the roots of equation lx^2 + nx + n = 0 be in ration p:q prove that {\displaystyle {\sqrt {~^{~}}}}p/q + q/p + n/l = 0
Soln:
Let the roots be pα and qα.
Then, pα + qα = –n/l and pα.qα = n/l
Now,
(pα+qα)/pα.qα = –(n/l)/(n/l)
Or, α(p+q)/α(pq) = –(n/l)
Or, p/pq + q/pq = –(n/l)
Or, p2/pq + q2/pq+ n/l = 0
So, p/q + q/p + n/l = 0