If the roots of the equation x2 + px + q = 0 are in the same ratio as those of the equation x2 + lx + m = 0, then p2m is equal to

Let the roots of each equation be in the ratio k:1 .Let kα and o be the roots of x2 + px + g = 0 .Then kα+α=−p and kα⋅α=q⇒ α=−pk+1 and α2=qk⇒    −pk+12=qk⇒k(k+1)2=qp2......(i)Again, let kβ and β be the roots of x2 + lx+ m =0Then, kβ+β=−I and kβ⋅β=m⇒ β=−1k+1 and β2=mk⇒  −1k+12=mk⇒ k(k+1)2=ml2......(ii)Thus, from Eqs. (i) and (ii), we getqp2    =ml2⇒     p2m    =I2q