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If HCF of (x2 + x – 12) and (2x2 – kx – 9) is (x – k), then value of k is
- a)–3
- b)3
- c)–4
- d)4
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If HCF of (x2 + x – 12) and (2x2 – kx – 9) is (x &nd...
∵ x – k is a factor of 2x2 – kx – 9
∴ 2k2 – k2 – 9 = 0
∴ k = ± 3
But factor of (x2 +x - 12) are (x+4),(x-3) Hence value of k is 3.
∴ 2k2 – k2 – 9 = 0
∴ k = ± 3
But factor of (x2 +x - 12) are (x+4),(x-3) Hence value of k is 3.
Most Upvoted Answer
If HCF of (x2 + x – 12) and (2x2 – kx – 9) is (x &nd...
Understanding the Problem
To find the value of k such that the highest common factor (HCF) of the polynomials (x² + x - 12) and (2x² - kx - 9) is (x - k), we need to analyze the given expressions.
Step 1: Factor the First Polynomial
The first polynomial is x² + x - 12. We can factor it:
- Factors of -12 that add up to +1 are +4 and -3.
- Thus, x² + x - 12 = (x + 4)(x - 3).
Step 2: HCF Analysis
The given HCF is (x - k). This means that (x - k) should be a factor of both polynomials.
Step 3: Substitute and Analyze the Second Polynomial
We need to ensure that (x - k) divides (2x² - kx - 9). For this, we apply polynomial division or substitute x = k:
- Substitute x = k into the second polynomial:
- 2(k)² - k(k) - 9 = 2k² - k² - 9 = k² - 9.
For (x - k) to be a factor, k² - 9 must equal zero:
- k² - 9 = 0
- This gives us k² = 9, leading to k = ±3.
Step 4: Identify the Correct Answer
Since the problem states the correct answer is option 'B', we choose k = 3.
Conclusion
Thus, the value of k is:
- k = 3 (option B).
This is consistent with the requirement that (x - k) be a factor of both polynomials.
To find the value of k such that the highest common factor (HCF) of the polynomials (x² + x - 12) and (2x² - kx - 9) is (x - k), we need to analyze the given expressions.
Step 1: Factor the First Polynomial
The first polynomial is x² + x - 12. We can factor it:
- Factors of -12 that add up to +1 are +4 and -3.
- Thus, x² + x - 12 = (x + 4)(x - 3).
Step 2: HCF Analysis
The given HCF is (x - k). This means that (x - k) should be a factor of both polynomials.
Step 3: Substitute and Analyze the Second Polynomial
We need to ensure that (x - k) divides (2x² - kx - 9). For this, we apply polynomial division or substitute x = k:
- Substitute x = k into the second polynomial:
- 2(k)² - k(k) - 9 = 2k² - k² - 9 = k² - 9.
For (x - k) to be a factor, k² - 9 must equal zero:
- k² - 9 = 0
- This gives us k² = 9, leading to k = ±3.
Step 4: Identify the Correct Answer
Since the problem states the correct answer is option 'B', we choose k = 3.
Conclusion
Thus, the value of k is:
- k = 3 (option B).
This is consistent with the requirement that (x - k) be a factor of both polynomials.
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If HCF of (x2 + x – 12) and (2x2 – kx – 9) is (x – k), then value of k isa)–3b)3c)–4d)4Correct answer is option 'B'. Can you explain this answer? for Railways 2025 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about If HCF of (x2 + x – 12) and (2x2 – kx – 9) is (x – k), then value of k isa)–3b)3c)–4d)4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Railways 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If HCF of (x2 + x – 12) and (2x2 – kx – 9) is (x – k), then value of k isa)–3b)3c)–4d)4Correct answer is option 'B'. Can you explain this answer?.
If HCF of (x2 + x – 12) and (2x2 – kx – 9) is (x – k), then value of k isa)–3b)3c)–4d)4Correct answer is option 'B'. Can you explain this answer? for Railways 2025 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about If HCF of (x2 + x – 12) and (2x2 – kx – 9) is (x – k), then value of k isa)–3b)3c)–4d)4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Railways 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If HCF of (x2 + x – 12) and (2x2 – kx – 9) is (x – k), then value of k isa)–3b)3c)–4d)4Correct answer is option 'B'. Can you explain this answer?.
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