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

Step-by-step solution

Given equation is ( -m) x^2+ x+1=0 Roots are , . One root is double the other. =2 Sum of roots = + 3 = - -m (2 )= 1 ( -m) ^2= ^2 9( -m)^2 2 ^2= 1 -m aligned & 2 ^2 9( -m)^2 = 1 ( -m) & 2 ^2 9( -m) =1 & 2 ^2=9( -m) 2 ^2-9 +9 m=0 aligned For to be real discriminant should be b^2-4 a c 081-4 2 9 m 0m 9 8 .