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