A root of the equation x2 - 4 = 0 is

2023

A root of the equation x2 - 4 = 0 is

Answer: D. More than one of the aboveConceptFor an equation of the form x2 = a with a > 0, the real roots are x = ±√a. Equivalently, a difference of squares factors as x2 − b2 = (x − b)(x + b).…

  1. A.

    2

  2. B.

    -2

  3. C.

    4

  4. D.

    More than one of the above

  5. E.

    None of the above

Show answer & explanation

Correct answer: D

Concept

For an equation of the form x2 = a with a > 0, the real roots are x = ±√a. Equivalently, a difference of squares factors as x2 − b2 = (x − b)(x + b).

Application

  1. Rearrange x2 − 4 = 0 as x2 = 4.

  2. Factor the difference of squares: x2 − 4 = (x − 2)(x + 2).

  3. By the zero-product rule, x − 2 = 0 or x + 2 = 0, giving x = 2 or x = −2.

Cross-check

Cross-check: substituting 2 gives 22 − 4 = 0, and substituting −2 gives (−2)2 − 4 = 0.

Therefore, two listed numerical values are roots, so the applicable choice is “More than one of the above.”

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