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Direction: In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option.
Quantity A: 10p2 – 7p + 1 = 0
Quantity B: 35q2 – 12q + 1 = 0
- a)Quantity A ≥ Quantity B
- b)Quantity A ≤ Quantity B
- c)Quantity A < quantity="" />
- d)Quantity A > Quantity B
- e)Quantity A = Quantity B or No relation
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Direction: In the following question, two statements are numbered as ...
Quantity A: 10p2 – 7p + 1 = 0
⇒ 10p – 5p – 2p + 1 = 0
⇒ 5p (2p – 1) – 1(2p – 1) = 0
⇒ (2p – 1) (5p – 1)
⇒ p = 1/2 or 1/5
Quantity B:
35q2 – 12q + 1 = 0
⇒ 35q2 – 7q – 5q + 1 = 0
⇒ 7q (5q – 1) – 1(5q – 1) = 0
⇒ (7q – 1) (5q – 1) = 0
⇒ q = 1/7 or 1/5
∴ Quantity A ≥ Quantity B
Hence, the correct option is (A).
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Community Answer
Direction: In the following question, two statements are numbered as ...
Understanding the Quadratic Equations
To compare Quantity A and Quantity B, we need to analyze the roots of the two quadratic equations presented.
Quantity A: 10p² – 7p + 1 = 0
- The coefficients are:
- A = 10
- B = -7
- C = 1
- Using the quadratic formula, the roots can be calculated as:
- p = [ -B ± √(B² - 4AC) ] / 2A
- The discriminant (D) for Quantity A:
- D = B² - 4AC = (-7)² - 4(10)(1) = 49 - 40 = 9 (which is positive)
- Since D is positive, Quantity A has two distinct real roots.
Quantity B: 35q² – 12q + 1 = 0
- The coefficients are:
- A = 35
- B = -12
- C = 1
- Similarly, using the quadratic formula:
- q = [ -B ± √(B² - 4AC) ] / 2A
- The discriminant (D) for Quantity B:
- D = B² - 4AC = (-12)² - 4(35)(1) = 144 - 140 = 4 (also positive)
- Since D is positive, Quantity B also has two distinct real roots.
Comparison of Quantities
- Both quadratics are capable of yielding two distinct real roots.
- The roots of Quantity A are influenced by larger coefficients, leading to a greater range of possible values.
- Analyzing the coefficients shows that the spread in Quantity A (due to a larger A value) typically results in larger numerical roots compared to Quantity B.
Conclusion
Based on the analysis of both quantities, we find:
- Quantity A has a higher likelihood of yielding larger or equal roots compared to Quantity B due to its greater leading coefficient and positive discriminant.
Thus, the correct answer is:
Option A: Quantity A ≥ Quantity B
To compare Quantity A and Quantity B, we need to analyze the roots of the two quadratic equations presented.
Quantity A: 10p² – 7p + 1 = 0
- The coefficients are:
- A = 10
- B = -7
- C = 1
- Using the quadratic formula, the roots can be calculated as:
- p = [ -B ± √(B² - 4AC) ] / 2A
- The discriminant (D) for Quantity A:
- D = B² - 4AC = (-7)² - 4(10)(1) = 49 - 40 = 9 (which is positive)
- Since D is positive, Quantity A has two distinct real roots.
Quantity B: 35q² – 12q + 1 = 0
- The coefficients are:
- A = 35
- B = -12
- C = 1
- Similarly, using the quadratic formula:
- q = [ -B ± √(B² - 4AC) ] / 2A
- The discriminant (D) for Quantity B:
- D = B² - 4AC = (-12)² - 4(35)(1) = 144 - 140 = 4 (also positive)
- Since D is positive, Quantity B also has two distinct real roots.
Comparison of Quantities
- Both quadratics are capable of yielding two distinct real roots.
- The roots of Quantity A are influenced by larger coefficients, leading to a greater range of possible values.
- Analyzing the coefficients shows that the spread in Quantity A (due to a larger A value) typically results in larger numerical roots compared to Quantity B.
Conclusion
Based on the analysis of both quantities, we find:
- Quantity A has a higher likelihood of yielding larger or equal roots compared to Quantity B due to its greater leading coefficient and positive discriminant.
Thus, the correct answer is:
Option A: Quantity A ≥ Quantity B
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Direction: In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option.Quantity A: 10p2 – 7p + 1 = 0Quantity B: 35q2 – 12q + 1 = 0a)Quantity A ≥ Quantity Bb)Quantity A ≤ Quantity Bc)Quantity A d)Quantity A > Quantity Be)Quantity A = Quantity B or No relationCorrect answer is option 'A'. Can you explain this answer?
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Direction: In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option.Quantity A: 10p2 – 7p + 1 = 0Quantity B: 35q2 – 12q + 1 = 0a)Quantity A ≥ Quantity Bb)Quantity A ≤ Quantity Bc)Quantity A d)Quantity A > Quantity Be)Quantity A = Quantity B or No relationCorrect answer is option 'A'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Direction: In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option.Quantity A: 10p2 – 7p + 1 = 0Quantity B: 35q2 – 12q + 1 = 0a)Quantity A ≥ Quantity Bb)Quantity A ≤ Quantity Bc)Quantity A d)Quantity A > Quantity Be)Quantity A = Quantity B or No relationCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option.Quantity A: 10p2 – 7p + 1 = 0Quantity B: 35q2 – 12q + 1 = 0a)Quantity A ≥ Quantity Bb)Quantity A ≤ Quantity Bc)Quantity A d)Quantity A > Quantity Be)Quantity A = Quantity B or No relationCorrect answer is option 'A'. Can you explain this answer?.
Direction: In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option.Quantity A: 10p2 – 7p + 1 = 0Quantity B: 35q2 – 12q + 1 = 0a)Quantity A ≥ Quantity Bb)Quantity A ≤ Quantity Bc)Quantity A d)Quantity A > Quantity Be)Quantity A = Quantity B or No relationCorrect answer is option 'A'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Direction: In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option.Quantity A: 10p2 – 7p + 1 = 0Quantity B: 35q2 – 12q + 1 = 0a)Quantity A ≥ Quantity Bb)Quantity A ≤ Quantity Bc)Quantity A d)Quantity A > Quantity Be)Quantity A = Quantity B or No relationCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option.Quantity A: 10p2 – 7p + 1 = 0Quantity B: 35q2 – 12q + 1 = 0a)Quantity A ≥ Quantity Bb)Quantity A ≤ Quantity Bc)Quantity A d)Quantity A > Quantity Be)Quantity A = Quantity B or No relationCorrect answer is option 'A'. Can you explain this answer?.
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