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Nature of Roots

If the equati...

Question

If the equation $(m - n) x^{2} + (n - l) x + l - m = 0$ has equal roots, then l, m and n satisfy.

A

2 l = m + n

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B

2 m = n + l

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C

m = n + l

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D

l = m + n

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Solution

The correct option is A $2 m = n + l$
$(m - n) x^{2} + (n - l) x + l - m = 0$
It has equal roots hence
$Δ = 0$
$(n - l)^{2} - 4 (e - m) (m - n) = 0$
$n^{2} + l^{2} - 2 l n - 4 (l m - m^{2} - l n + m n) = 0$
$n^{2} + l^{2} - 2 l n - 4 l m + 4 m^{2} + 4 l n - 4 m n = 0$
$n^{2} + l^{2} + 2 l n + 4 m^{2} - 4 l m - 4 m n = 0$
$(n + l - 2 m)^{2} = 0$
$n + l = 2 m$

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