If 6 lies between the roots of the equation x2+2(a−3)x+9=0 then

Let f(x)=x2+2(a−3)x+9If 6 lies between the roots of f(x) =O,then we must have Disc> 0, and (ii) f (6) < 0⇒ 4(a−3)2−36>0⇒ (a−3)2−9>0⇒ a2−6a>0⇒ a(a−6)>0⇒a<0 or a>6 and,  f(6)<0⇒ 36+12(a−3)+9<0⇒a<−34a<−3/4 i.e. a∈(−∞,−3/4)