Compare x and y (define the answer codes): I. 8x^2 + 6x = 5 II. 12y^2 − 22y + 8 = 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:
Each quadratic yields two real roots. Unless one interval of roots lies entirely above or below the other, the pairwise comparison will depend on which roots are chosen. We compute exact roots to check for consistent ordering.

Given Data / Assumptions:

• I: 8x^2 + 6x − 5 = 0.
• II: 12y^2 − 22y + 8 = 0.
• Any real root from each equation may be chosen independently.

Concept / Approach:
Apply the quadratic formula to both equations and list all roots. Examine whether a single inequality holds across every combination of choices; if not, the relationship is indeterminate.

Step-by-Step Solution:

Verification / Alternative check:
Construct a 2×2 table of choices confirming equality in one pair and strict inequalities in others with different directions.

Why Other Options Are Wrong:

• x > y, x < y, x = y: Each is true for some particular pairing, but not for all pairings.

Common Pitfalls:
Assuming the principal (greater) root is always chosen; the problem statement allows any root, making a single comparison impossible.

Final Answer: