# Chapter 9 - Quadratic Functions and Equations - 9-3 Solving Quadratic Equations - Practice and Problem-Solving Exercises - Page 551: 41

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.

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