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
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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
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
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