Solve equations (i). a2 + 11a + 30 = 0 and (ii). b2 + 6b + 5 = 0 to determine a and b?
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Answer: B. If a ≤ b
Explanation
Factoring the first quadratic equation produces roots of negative five and negative six for variable a. Factoring the second quadratic equation produces roots of negative one and negative five for variable b. Comparing every possible root combination demonstrates that all values of a are consistently less than or equal to corresponding values of b. Quadratic root analysis involves finding all domain values that satisfy polynomial equations set equal to zero. Comparative inequality testing across multiple roots requires evaluating every possible pair combination between the two sets. Negative numbers follow a reverse magnitude order where values closer to zero are strictly greater than more negative values.
Option A is incomplete because it ignores the instances where both variables share equal root values. Option C is incorrect because a definitive and consistent inequality relationship can be successfully established. Option D contradicts the negative number line rules since negative six is smaller than negative five.
- Subject
- Mathematics
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- Mathematics
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- Difficulty
- medium
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