Let x be the greater real root of x^2 − 8x + 15 = 0 and y be the greater real root of y^2 − 3y + 2 = 0. Compare x and y.

Introduction / Context:
Both quadratics factor neatly. After identifying the larger root in each case, a simple comparison yields the correct relation between x and y.

Given Data / Assumptions:

• x^2 − 8x + 15 = 0 ⇒ (x − 3)(x − 5) = 0 ⇒ greater x = 5.
• y^2 − 3y + 2 = 0 ⇒ (y − 1)(y − 2) = 0 ⇒ greater y = 2.

Concept / Approach:
Factor, select the greater root, compare numerically.

Step-by-Step Solution:

Verification / Alternative check:
The quadratic formula yields identical values; factoring is quickest.

Why Other Options Are Wrong:
They contradict the numerical ordering 5 > 2.

Common Pitfalls:
Accidentally picking the smaller root in either quadratic.

Final Answer:
If x > y