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.
Aptitude
Quadratic Equation
Difficulty: Easy
Choose an option
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AIf x > y
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BIf x ≥ y
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CIf x < y
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DIf x ≤ y
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EIf x = y
Answer
Correct Answer: If x > y
Explanation
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:
x = 5; y = 2.Therefore x > y.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