Which equations are true for [tex]\( x = -2 \)[/tex] and [tex]\( x = 2 \)[/tex]? Select two options:

A. [tex]\( x^2 - 4 = 0 \)[/tex]

B. [tex]\( x^2 = -4 \)[/tex]

C. [tex]\( 3x^2 + 12 = 0 \)[/tex]

D. [tex]\( 4x^2 = 16 \)[/tex]

E. [tex]\( 2(x - 2)^2 = 0 \)[/tex]



Answer :

Sure, let's examine each equation with the given values [tex]\( x = -2 \)[/tex] and [tex]\( x = 2 \)[/tex] to determine which of them hold true.

1. Equation: [tex]\( x^2 - 4 = 0 \)[/tex]

For [tex]\( x = -2 \)[/tex]:
[tex]\[ (-2)^2 - 4 = 4 - 4 = 0 \][/tex]
So, the equation is true for [tex]\( x = -2 \)[/tex].

For [tex]\( x = 2 \)[/tex]:
[tex]\[ 2^2 - 4 = 4 - 4 = 0 \][/tex]
So, the equation is also true for [tex]\( x = 2 \)[/tex].

Therefore, [tex]\( x^2 - 4 = 0 \)[/tex] is true for both [tex]\( x = -2 \)[/tex] and [tex]\( x = 2 \)[/tex].

2. Equation: [tex]\( x^2 = -4 \)[/tex]

For [tex]\( x = -2 \)[/tex]:
[tex]\[ (-2)^2 = 4 \neq -4 \][/tex]
So, the equation is not true for [tex]\( x = -2 \)[/tex].

For [tex]\( x = 2 \)[/tex]:
[tex]\[ 2^2 = 4 \neq -4 \][/tex]
So, the equation is also not true for [tex]\( x = 2 \)[/tex].

Therefore, [tex]\( x^2 = -4 \)[/tex] is not true for either [tex]\( x = -2 \)[/tex] or [tex]\( x = 2 \)[/tex].

3. Equation: [tex]\( 3x^2 + 12 = 0 \)[/tex]

For [tex]\( x = -2 \)[/tex]:
[tex]\[ 3(-2)^2 + 12 = 3 \cdot 4 + 12 = 12 + 12 = 24 \neq 0 \][/tex]
So, the equation is not true for [tex]\( x = -2 \)[/tex].

For [tex]\( x = 2 \)[/tex]:
[tex]\[ 3 \cdot 2^2 + 12 = 3 \cdot 4 + 12 = 12 + 12 = 24 \neq 0 \][/tex]
So, the equation is also not true for [tex]\( x = 2 \)[/tex].

Therefore, [tex]\( 3x^2 + 12 = 0 \)[/tex] is not true for either [tex]\( x = -2 \)[/tex] or [tex]\( x = 2 \)[/tex].

4. Equation: [tex]\( 4x^2 = 16 \)[/tex]

For [tex]\( x = -2 \)[/tex]:
[tex]\[ 4(-2)^2 = 4 \cdot 4 = 16 \][/tex]
So, the equation is true for [tex]\( x = -2 \)[/tex].

For [tex]\( x = 2 \)[/tex]:
[tex]\[ 4 \cdot 2^2 = 4 \cdot 4 = 16 \][/tex]
So, the equation is also true for [tex]\( x = 2 \)[/tex].

Therefore, [tex]\( 4x^2 = 16 \)[/tex] is true for both [tex]\( x = -2 \)[/tex] and [tex]\( x = 2 \)[/tex].

5. Equation: [tex]\( 2(x-2)^2 = 0 \)[/tex]

For [tex]\( x = -2 \)[/tex]:
[tex]\[ 2(-2-2)^2 = 2(-4)^2 = 2 \cdot 16 = 32 \neq 0 \][/tex]
So, the equation is not true for [tex]\( x = -2 \)[/tex].

For [tex]\( x = 2 \)[/tex]:
[tex]\[ 2(2-2)^2 = 2 \cdot 0 = 0 \][/tex]
So, the equation is true for [tex]\( x = 2 \)[/tex].

Therefore, [tex]\( 2(x-2)^2 = 0 \)[/tex] is true only for [tex]\( x = 2 \)[/tex].

The equations that are true for the given values [tex]\( x = -2 \)[/tex] and [tex]\( x = 2 \)[/tex] are:
- [tex]\( x^2 - 4 = 0 \)[/tex]
- [tex]\( 4x^2 = 16 \)[/tex]
- [tex]\( 2(x-2)^2 = 0 \)[/tex]

Hence, the correct options are:
- [tex]\( x^2 - 4 = 0 \)[/tex]
- [tex]\( 4x^2 = 16 \)[/tex]
- [tex]\( 2(x-2)^2 = 0 \)[/tex]