Solve equations I. a2 + 8a + 16 = 0 and II. b2 – 4b + 3 = 0 to determine a and b?
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Answer: A. If a < b
Explanation
The correct answer is a is less than b because all roots of a are smaller than b. Solving equation one yields a single root value of negative four. Solving equation two yields root values of positive one and positive three. Quadratic equations are solved by factoring or using the standard quadratic formula. Equation one factors into the squared binomial a plus four squared equals zero. Equation two factors into b minus one multiplied by b minus three equals zero.
Inequality comparison problems are common in competitive aptitude and reasoning tests. Algebraic root analysis helps determine domain restrictions in advanced calculus functions. Engineering optimization models use quadratic equations to find critical minimum points. Option B is incorrect because a is strictly less than b, not less than or equal. Option C fails because a definitive relationship between a and b can be established. Option D is wrong because negative four is smaller than both one and three.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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