Answer :
To find which numbers are solutions to the equation [tex]\(x^2 = -7\)[/tex], we need to determine if any real numbers, when squared, result in [tex]\(-7\)[/tex].
1. Understanding the equation:
- The equation [tex]\(x^2 = -7\)[/tex] means we are looking for a number [tex]\(x\)[/tex] that, when squared, equals [tex]\(-7\)[/tex].
- Squaring a real number always gives a non-negative result (zero or positive), because multiplying two positive numbers or two negative numbers results in a positive number.
2. Evaluating each option:
- A. [tex]\(-\sqrt{7}\)[/tex]:
[tex]\((- \sqrt{7})^2 = (\sqrt{7})^2 = 7\)[/tex]. This is not equal to [tex]\(-7\)[/tex].
- B. 49:
[tex]\(49^2 = 2401\)[/tex]. This result is not [tex]\(-7\)[/tex].
- C. [tex]\(-3.5\)[/tex]:
[tex]\((-3.5)^2 = 12.25\)[/tex]. This is not equal to [tex]\(-7\)[/tex].
- D. [tex]\(\sqrt{7}\)[/tex]:
[tex]\((\sqrt{7})^2 = 7\)[/tex]. This is not equal to [tex]\(-7\)[/tex].
- E. [tex]\(-7\)[/tex]:
[tex]\((-7)^2 = 49\)[/tex]. This is not equal to [tex]\(-7\)[/tex].
3. Conclusion:
Since squaring any real number gives a non-negative value and [tex]\(-7\)[/tex] is negative, there are no real numbers that satisfy the equation [tex]\(x^2 = -7\)[/tex].
Thus, no real-number solutions exist for this equation, and the correct answer is F. None of these.
1. Understanding the equation:
- The equation [tex]\(x^2 = -7\)[/tex] means we are looking for a number [tex]\(x\)[/tex] that, when squared, equals [tex]\(-7\)[/tex].
- Squaring a real number always gives a non-negative result (zero or positive), because multiplying two positive numbers or two negative numbers results in a positive number.
2. Evaluating each option:
- A. [tex]\(-\sqrt{7}\)[/tex]:
[tex]\((- \sqrt{7})^2 = (\sqrt{7})^2 = 7\)[/tex]. This is not equal to [tex]\(-7\)[/tex].
- B. 49:
[tex]\(49^2 = 2401\)[/tex]. This result is not [tex]\(-7\)[/tex].
- C. [tex]\(-3.5\)[/tex]:
[tex]\((-3.5)^2 = 12.25\)[/tex]. This is not equal to [tex]\(-7\)[/tex].
- D. [tex]\(\sqrt{7}\)[/tex]:
[tex]\((\sqrt{7})^2 = 7\)[/tex]. This is not equal to [tex]\(-7\)[/tex].
- E. [tex]\(-7\)[/tex]:
[tex]\((-7)^2 = 49\)[/tex]. This is not equal to [tex]\(-7\)[/tex].
3. Conclusion:
Since squaring any real number gives a non-negative value and [tex]\(-7\)[/tex] is negative, there are no real numbers that satisfy the equation [tex]\(x^2 = -7\)[/tex].
Thus, no real-number solutions exist for this equation, and the correct answer is F. None of these.
