<p>The range of values of '<i>a</i>' such that \(\sqrt{x} = x^2 + a\) is satisfied for maximum number of values of '<i>x</i>'</p>
Step-by-Step Solution
Key Concept: Graphically analyze the intersection of a square root function and a parabola to determine when maximum intersections occur.
<p>We seek the intersection of $y = \sqrt{x}$ and $y = x^2 + a$. For maximum intersections, we analyze when the parabola $y = x^2 + a$ intersects the square root curve at the most points. The parabola must be positioned such that it intersects $y = \sqrt{x}$ at multiple points. This occurs when the parabola is shifted downward, i.e., when $a < -1$.</p>
Correct Answer: A