Solve equations (i). a2 – 9a + 20 = 0 and (ii). 2b2 – 5b – 12 = 0 to determine a and b?
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Answer: D. If a ≥ b
Explanation
Solving the first equation yields roots four and five for variable a. Solving the second equation yields roots four and negative 1.5 for variable b. Comparing every possible root combination shows that a is always greater than or equal to b. Quadratic equations are solved using factoring or the standard quadratic formula method. Equation one factors into a minus 4 times a minus 5 equaling zero. Equation two factors into 2b plus 3 times b minus 4 equaling zero.
Quadratic inequality comparisons are standard components of quantitative aptitude tests. Engineers use root analysis to determine stability thresholds in physical systems. Comparing solution sets helps verify boundaries in algebraic modeling. Choosing a less than b contradicts the instances where a equals or exceeds b. Choosing a less than or equal to b ignores the higher root values of a. Choosing an unestablished relationship ignores the clear numerical dominance of the roots.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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