Complex Numbers And Quadratic Equations question 795
Question: If the equation $ (m-n)x^{2}+(n-l)x+l-m=0 $ has equal roots, then l, m and n satisfy [DCE 2002]
Options:
A) $ 2l=m+n $
B) $ 2m=n+l $
C) $ m=n+l $
D) $ l=m+n $
Show Answer
Answer:
Correct Answer: B
Solution:
Roots are equal so $ b^{2}-4ac=0 $
Þ $ {{(n-l)}^{2}}-4(m-n)(l-m)=0 $
Þ $ n^{2}+l^{2}-2nl-4(ml-nl-m^{2}+mn)=0 $
Þ $ n^{2}+l^{2}-2nl-4ml+4nl+4m^{2}-4mn=0 $
Þ $ l^{2}+n^{2}+{{(2m)}^{2}}+2nl-4mn-4ml=0 $
Þ $ {{(l+n-2m)}^{2}}=0 $
Þ $ l+n=2m $
Þ l, m, n are in A.P.
BETA
