If the ratio of the roots of the equation x2+px+q=0  be same as that of the roots of the equation x2+lx+m=0  then

The given equations are x2+px+q=0 ……. ( 1 ) And x2+lx+m=0  …… ( 2 )Let the roots of the two equations be α,β  and γ,δ  respectively,From Eq.( 1 ):Some of the roots  α+β=−p, Product of the roots   αβ=q   From Eq.( 2 ):Some of the roots  γ+δ=−l, Product of the roots   γδ=m By the given condition,   αβ=  γδ  ⇒  =α+βα−β=  γ+δγ−δ Squaring on both sides⇒      (α+β)2(α−β)2  =  (γ+δ)2(γ−δ)2 ⇒    (α+β)2(α+β)2−4αβ=    (γ+δ)2(γ+δ)2−4γδ ⇒    p2p2−4q=  l2l2−4m ⇒    p2l2−4p2m=  l2p2−4l2q ⇒    p2m  =l2q.