If one root of the equation ((l- m ) x ^2+l x +1=0 ) is double of the other and if (l ) is real then the greatest value of ( m ) is ((l m ) ) :

Step-by-step solution

Let the roots of the equation be ( ) and (2 ), then ( +2 = l ~m -l and 2 = 1 l- m ) ( = l 3( ~m -l) and ^2= 1 2(l- m ) . ) Eliminating ( ), we get ( l^2 9( ~m -l)^2 = 1 2(l- m ) 2 l^2-9 l+9 ~m =0 ) Since (l ) is real, so ((-9)^2-4 2 9 ~m 0 ) ( m 9 8 )