if the ratio of the roots of the equation x^{2}+px+q=0 is equal to the ratio of the roots of the equation x^{2}+lx+m=0, prove that mp^{2}=ql^{2}

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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