Solve equations I. x2 + 11x + 30 = 0 and II. y2 + 15y + 56 = 0 to determine x and y?
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Answer: B. If x > y
Explanation
Solving equation one yields roots of negative five and negative six through standard factoring methods. Solving equation two yields roots of negative seven and negative eight by factoring the quadratic expression. Comparing all resulting roots shows that every possible value of x is greater than y, confirming x greater than y. Quadratic inequality comparisons require finding all possible roots for both equations before evaluating ranges. Negative numbers closer to zero possess greater numerical value than more negative integers further down. Systematic root comparison determines relative ordering constraints between two independent quadratic variables.
Comparative analysis in mathematics tests relationships between variables governed by different quadratic constraints. Optimization problems often compare multiple equation models to determine superior parameter ranges. Algorithmic decision making relies on relational evaluations of paired mathematical variables. Option A contradicts the root comparison since the smaller x roots are still larger than y roots. Option C fails because the strict greater than relationship holds true across all root pairings. Option D is incorrect because x values are strictly greater without any possible equality overlap.
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- Mathematics
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- Mathematics
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