Solve equations I. 9a2 + 18a + 5 = 0 and II. 2b2 + 13b + 20 = 0 to determine a and b?
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Answer: A. If a > b
Explanation
Solving the first quadratic equation gives roots that are strictly positive and relatively large numbers. Solving the second quadratic equation yields roots that are significantly smaller than the first roots. Comparing every possible root from the first equation confirms each value exceeds the second equation values. Quadratic equations take the standard algebraic form of ax squared plus bx plus c equals zero. Finding the roots involves factoring the polynomial expression or applying the quadratic formula carefully every time. Inequality comparisons between two sets of roots require checking all combinations of solutions systematically.
Comparing ranges of values is fundamental when analyzing conflicting economic indicators or competing mathematical models. Engineers frequently evaluate multiple system states to ensure one operational parameter consistently dominates another. Mastering inequality analysis helps students transition smoothly into advanced calculus and linear programming courses. Option B suggests non-strict inequality which fails because equality never occurs between any computed roots. Option C incorrectly reverses the relationship by claiming the first variable is smaller than the second. Option D claims a non-strict reverse inequality that completely contradicts the actual calculated root values.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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