(a) The equation
has two irrational solutions.
(b) The equation
has one rational solution.
(c) The equation
has two irrational solutions.
(d) The equation
has two imaginary solutions.
(e) The equation
has two imaginary solutions.
Explanation:
(a) Solving the equation
, we get the solutions,
and 
Thus,
and 
Hence, the equation
has two irrational solutions.
(b) Solving the equation
, we get the solution,

Hence, the equation
has one rational solution.
(c) Solving the equation
, we get the solutions,
and 
Thus,
and 
Hence, the equation
has two irrational solutions.
(d) Solving the equation
, we get the solutions,
and 
Hence, the equation
has two imaginary solutions.
(e) Solving the equation
, we get the solutions,
and 
Hence, the equation
has two imaginary solutions.