CPM Homework Help : INT2 Problem 6-75

Without completely solving them, decide which of the following equations have real solutions and which have complex solutions.

Hint:

In parts (a), (b), (e), and (f), move the constant term to the other side of the equation.
What will happen if you try to take the square root of both sides?
In parts (c) and (d) you can begin to complete the square.

$0 = x^2 - 6$
Answer (a):
real

$0 = x^2 + 6$
Answer (b):
complex

$0 = x^2 - 2x + 10$
Answer (c):
complex

$0 = x^2 - 2x - 10$
Answer (d):
real

$0 = (x - 3)^2 - 4$
Answer (e):
real

$0 = (x - 3)^2 + 4$
Answer (f):
complex