Question

If the roots of the quadratic equation p(q-r)x2+q(r-p)x+r(p-q)=0are equal ,show that 1/p+1/r=2/q

Answer 1

roots equal mean D=b^2-4ac=0
now
q^2 (r-p)^2=4pr (q-r)(p-q)

actually this is possible only when pq, qr and rp are in AP

so,
use concept of AP
common difference =constant
=> qr-pq=rp-qr
=> 2qr=rp+pq
=> pq+rp=2qr
divided both side pqr
=> pq/pqr +rp/pqr=2qr/pqr
=> 1/r+1/q=2/p