if the ratio of the roots of the equation x2+px+q=0 is equal to the ratio of the roots of the equation x2+lx+m=0, prove that mp2=ql2

Let α and β be the roots of equation

x 2 + px + q = 0

and a and b be the roots of equation

x 2 + lx + m = 0

Then α + β = – p, αβ = q ......(1)

a + b = – l, ab = m ......(2)

Given

Adding (3) and (4), we get

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