Solve equations I. a2 – 13a + 42 = 0 and II. b2 – 15b + 56 = 0 to determine a and b?
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Answer: D. If a ≤ b.
Explanation
The correct answer is a is less than or equal to b across all compared roots. Solving equation one yields roots of six and seven for variable a. Solving equation two yields roots of seven and eight for variable b. Quadratic roots are found by factoring the polynomial into two binomial expressions. Equation one factors into a minus six multiplied by a minus seven equals zero. Equation two factors into b minus seven multiplied by b minus eight equals zero.
Comparative inequality analysis for quadratic roots is standard in quantitative aptitude tests. Mathematical modeling uses root comparisons to establish boundaries for system variables. Engineering design limits are often evaluated using root inequalities for stability. Option A is incorrect because a values are never greater than b values. Option B is wrong because a is not greater than or equal to b in all cases. Option C is incomplete because a can sometimes equal b when both equal seven.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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