A
Exactly one
B
Exactly two
C
Infinitely many
D
Zero
Explanation
Correct answer: D.
Choice D is correct. Since the square of a real number is never negative, the given equation isn't true for any real value of . Therefore, the given equation has zero distinct real solutions.
Desmos solution:
Note: Graph the blue parabola and the green horizontal line; they never intersect, so there are zero real solutions.
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
Choice A is incorrect and may result from conceptual or calculation errors.
Choice B
Choice B is incorrect and may result from conceptual or calculation errors.
Choice C
Choice C is incorrect and may result from conceptual or calculation errors.