(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.