Question

Find the roots of the equation
l^2 (m^2-n^2)x^2 + m^2(n^2-l^2)x + n^2 (l^2-m^2) =0

Answer 1

Dear student,
Observe that $l^2(m^2-n^2)+m^2(n^2-l^2)+n^2(l^2-m^2)=0$
Hence x=1 is one root
Let other root be $\alpha$
Now product of roots =$\alpha$
$Hence\alpha =\frac{n^2(l^2-m^2)}{l^2(m^2-n^2)}$
Hence the roots are $1,\frac{n^2(l^2-m^2)}{l^2(m^2-n^2)}$
Regards
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