if you square root 1, is the answer plus or minus 1 or just 1?

Question

The problem is: Find the zeros of the quadratic equation using the square root method.

 

g(x)=(x+2)² -1

 

I have solved:

(x+2)² -1=0

 

√(x+2)² = √1

 

x+2=1

 

I'm not sure if it should be plus or minus 1 or just 1. 

Answer 1

When you take the square root of a number, you should remember that it is both the positive and negative. For example, the square root of 4 is +/- 2. Squaring 2 gives you 4, as does squaring (-2). (-2)*(-2)=4 Squaring is a classic case of a double negative. I hope this helps!

Answer 2

Two conventions are held.

The example you give is the one that relates to solutions. If the second line of you solution used the difference of squares:

(x + 2 + 1)(x + 2 - 1) = 0

(x + 3)(x -+ 1) = 0

x ∈ {-3, 1}

 

Two solutions exist. This would occur also using the Quadratic Formula.

So when solving equations, both roots are taken.

 

The second convention deal with the radical standing alone. It is only the positive root unless requested, e.g.,

√16 = 4

-√16 = -4

±√16 = ±4