Solve equations I. x2 – x – 42 = 0 and II. y2 – 17y + 72 = 0 to determine x and y?
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Answer: A. If x < y
Explanation
The correct answer is x is less than y because all x roots are smaller than y roots. Solving equation one yields roots of positive seven and negative six. Solving equation two yields roots of positive eight and positive nine. Quadratic equations are solved by finding two numbers that multiply to the constant and add to the coefficient. Equation one factors into x minus seven multiplied by x plus six equals zero. Equation two factors into y minus eight multiplied by y minus nine equals zero.
Comparing roots of quadratic equations tests advanced algebraic manipulation skills. Physics modeling uses quadratic roots to determine projectile landing time intervals. Economic forecasting applies quadratic equations to model supply and demand equilibrium points. Option B is incorrect because x values are smaller than y values, not larger. Option C is wrong because x is strictly less than y across all root comparisons. Option E is incorrect because a clear and definitive relationship is successfully established.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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