Answer
Two Solutions: n > 0
One Solution: n = 0
No solutions: n < 0
Work Step by Step
TWO SOLUTIONS: This equation will have two solutions for all values of n that are greater than zero because these values will have a positive and negative solution. Example:
$x^{2}$ = n, where n = 4
$x^{2}$ = 4
x = 2, -2
$x^{2}$ = n, where n = 1
$x^{2}$ = 1
x = 1, -1
Each of these equations has two solutions because the solutions will always consist of a positive and negative number.
ONE SOLUTION: This equation will only have one solution for n = 0 because all values greater than zero will yield two solutions and all values less than zero will yield no solutions. Example:
$x^{2}$ = n, where n = 0
$x^{2}$ = 0
x = 0
NO SOLUTIONS: This equation will have no solutions for all values of n that are less than zero because you cannot square any number and get a negative solution. Example:
$x^{2}$ = n, where n = -1
$x^{2}$ = -1
$x^{2}$ $\ne$ -1
There is no number you can square that will yield a negative solution. Therefore, all numbers less than zero will have no solution.
