Question

Which equations are true for x = -2 and x = 2? Select two options

A x²-4=0

B x²=-4

B 3x² + 12 = 0

C 4x² = 16

D 2(x-2)² = 0

Answer 1

A and C

Explanation:

solving the equations

A

x² - 4 = 0 ( add 4 to both sides )

x² = 4 ( take square root of both sides )

x = ±
`√(4)` = ± 2 ← required solution

B

x² = - 4 ← has no real solutions

C

4x² = 16 ( divide both sides by 4 )

x² = 4 ( take square root of both sides )

x = ±
`√(4)` = ± 2 ← required solution

D

2(x - 2)² = 0 , then

x- 2 = 0 ( add 2 to both sides )

x = 2 ← not the required solution

Answer 2

Answer A and C

Explanation:

Let us solve the equations one by one and let us check whether the answers are matching with the answers given in the questions.

A) x² - 4 = 0

( x² - 2² ) = 0

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

∴ x - 2 = 0 or x + 2 = 0

x = 2 x = -2 ( Matched )

B) x² = -4

x = ±√-4 ← no real solutions (Not matched )

B) 3x² + 12 = 0

3 ( x² + 4 ) = 0

3 ( x² + 2² ) = 0 ← no real solutions (Not matched)

C) 4x² = 16

Divide both sides by 4.

x² = 4

x = ±√4

∴ x = 2 or x = -2 (Matched)

D) 2 ( x - 2 )² = 0

(2x - 4)² = 0

4x² - 16x + 16 = 0

Divide the whole equation by 4.

x² - 4x + 4 = 0

x² - 2x - 2x + 4 = 0

x ( x - 2 ) - 2 ( x - 2 ) = 0

( x - 2 ) ( x - 2) =

∴ x - 2 = 0 or x - 2 = 0

x = 2 x = 2 ( Not matched )