The values of 'a'  for which the expression  x2−(3a−1)x+2a2+2a−11  is always positive are given

The given expression is x2−(3a−1)x+2a2+2a−11 …. ( 1 )From Eq.( 1 ):  the coefficient of x2>0.Hence, the given expression will assume positive values only if  Δ<0From Eq.( 1 ):  a=1, b=−(3a−1), c=2a2+2a−11b2−4ac<0⇒{−(3a−1)2}−4×1×(2a2+2a−11)<0⇒    9a2−6a+1−8a2−8a+44<0⇒    a2−14a+45<0⇒    (a−5)(a−9)<0 ⇒  5