The value of a from which one root of equation e^a x^2 - e^2 ax +e^a -1=0 lies between 1 and 2 are given by

let the polynomial on the LHS be f(x), (f(2)/f(1))<0,upon simplification, we get 4e^a -2e^2a +e^a -1>0

solving this quadratic inequality in e^a =y, we get (5-√17)/4<y<(5+√17)/4,therefore

ln((5-√17)/4)<a<ln((5+√17)/4)

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