Compare x and y (define the answer codes): I. 18x^2 + 18x + 4 = 0 II. 12y^2 + 29y + 14 = 0 x and y are real roots (any root from each). Choose: A) x > y B) x < y C) x = y D) Relationship cannot be determined

Introduction / Context:
This comparison asks us to pick one root from each quadratic and compare them. Since each quadratic has two distinct real roots, the relationship may depend on which roots are chosen unless a strict ordering holds across all combinations. We must compute the roots or characterize their ranges.

Given Data / Assumptions:

• I: 18x^2 + 18x + 4 = 0 ⇒ 9x^2 + 9x + 2 = 0.
• II: 12y^2 + 29y + 14 = 0.
• Any real root x from I and any real root y from II can be selected.

Concept / Approach:
Find both roots for each quadratic using the quadratic formula and list their numerical values. If there is overlap (equality) or changing order depending on choices, the relationship cannot be uniquely determined.

Step-by-Step Solution:

Verification / Alternative check:
Tabulate pairs to see the variability. The presence of equality (−2/3 equals −2/3) already prevents a strict inequality conclusion.

Why Other Options Are Wrong:

• x > y, x < y, x = y: Each can occur for specific choices, but none holds universally across all root pairings.

Common Pitfalls:
Assuming a single root per equation or overlooking that either root may be picked. For comparison questions, confirm if the order is consistent for all combinations.

Final Answer: