For a,b,c R if ax^2+ bx+c is real for real values of x and imaginary for imaginary values of x then:
a) a > 0 b) a < 0 c) a = 0 d) None of these

• ax^2+bx+c=x(ax+b)+c
  as a,b,c are real
  if x is real then expression will be real for all value of x
  but
  if x is imaginary then expression will be imaginary only when one of x and ax+b
  is real if we consider all value of x
  so x can't be real (given imaginary)
  then ax+b should be real
  so a=0 ans.
• 12 years agoHelpfull: Yes(18) No(6)
• when x is real
  for any value of a either its >,< or = 0 expression will be real
  and when x is imaginary
  for any value of a it will be imaginary
  on the other hand for b=0 expression will be real for even imaginary value of x
  So, the expression is dependent on b for being real or imaginary not on a
  hence ans is d) None of these
• 12 years agoHelpfull: Yes(4) No(0)
• c) a=0.
  if b= real value => b+c real
  if b= 2+3i => b+c =(2+c)+3i
• 12 years agoHelpfull: Yes(2) No(8)