Let x be the greater real root of x^2 − x − 12 = 0 and y be the greater real root of y^2 + 5y + 6 = 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: Straightforward factoring reveals both sets of roots, and the greater ones are compared directly as per the clarified convention.
Given Data / Assumptions:
- x^2 − x − 12 = 0 ⇒ (x − 4)(x + 3) = 0 ⇒ greater x = 4.
- y^2 + 5y + 6 = 0 ⇒ (y + 2)(y + 3) = 0 ⇒ greater y = −2.
Concept / Approach: Factor both quadratics. Identify greater real roots. Compare numerically.
Step-by-Step Solution:
x = 4; y = −2.Hence x > y.Verification / Alternative check: Plugging back confirms each value solves the respective equation.
Why Other Options Are Wrong: They contradict 4 > −2.
Common Pitfalls: Picking the smaller root for either quadratic or sign mistakes during factoring.
Final Answer: If x > y