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 above — ConceptFor 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).…
- A.
2
- B.
-2
- C.
4
- D.
More than one of the above
- 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
Rearrange x2 − 4 = 0 as x2 = 4.
Factor the difference of squares: x2 − 4 = (x − 2)(x + 2).
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.”