The least value of a  for which the roots of the equation  x2−2x−log4a=0  are real is

The given equation is x2−2x−log4a=0 Given that the roots are real ⇒ dicriminant ≥ 0Let a=1,b=−2,c=-log4a⇒(−2)2+4.1.  log4a≥0        (∵  b2−4ac≥0)⇒4log4a≥−4⇒log4a≥−1  ⇒ a≥4−1⇒ a≥14.hence, least value of a   is 14 .