Question

If $\alpha$ and $\beta$ are the roots of the quadratic equation $(l-m)x^2+(m-n)x+(n-l)=0$ and 2l =m+n, then what is the relation between $\alpha$ and $\beta$?

Answer 1

$\alpha +\beta =-\frac{(m-n)}{l-m}---\left(i\right)\alpha \beta =\frac{(n-l)}{l-m}---\left(ii\right)$
2l = m + n
l + l = m + n
l -m = n - l ----(iii)
Substitute the value of l - m in eq(ii) we get,
$\alpha \beta =\frac{(l-m)}{(l-m)}$
$\alpha \beta =1$