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In this question, a statement of Assertion (A) is followed by a statement of Reason (R).
Assertion (A): The value of k for which x - 2 is a factor of x³-3x² + k is 4. 1
Reason (R): If f(x) is a polynomial of degree greater than or equal to 1 and a is a real number, thenx - a is a factor of f(x) if f(a) = 0.?
Assertion (A): The value of k for which x - 2 is a factor of x³-3x² + k is 4. 1
Reason (R): If f(x) is a polynomial of degree greater than or equal to 1 and a is a real number, thenx - a is a factor of f(x) if f(a) = 0.?
Most Upvoted Answer
In this question, a statement of Assertion (A) is followed by a statem...
Assertion and Reason Explanation:
Assertion (A):
The value of k for which x - 2 is a factor of x³-3x² + k is 4.
Reason (R):
If f(x) is a polynomial of degree greater than or equal to 1 and a is a real number, then x - a is a factor of f(x) if f(a) = 0.
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Explanation:
Understanding Assertion (A):
- The given polynomial is x³-3x² + k.
- If x - 2 is a factor of this polynomial, it means that when x = 2, the polynomial should equal 0.
- Substituting x = 2 in the polynomial, we get: 2³ - 3(2)² + k = 0.
- Solving this equation gives us k = 4, which satisfies the condition for x - 2 to be a factor.
Understanding Reason (R):
- If x - a is a factor of a polynomial f(x), it implies that f(a) = 0.
- This is based on the factor theorem which states that if a polynomial f(x) is divided by x - a, the remainder is 0.
- Therefore, when x = a, the polynomial f(x) evaluates to 0, indicating that x - a is indeed a factor of f(x).
Conclusion:
- The given assertion is true because when k = 4, x - 2 becomes a factor of the polynomial x³-3x² + k.
- The reason provided is also valid as it explains the general concept behind factors of a polynomial based on the factor theorem.
- Hence, both the assertion and reason are correct, and the reason is the correct explanation for the assertion.
Assertion (A):
The value of k for which x - 2 is a factor of x³-3x² + k is 4.
Reason (R):
If f(x) is a polynomial of degree greater than or equal to 1 and a is a real number, then x - a is a factor of f(x) if f(a) = 0.
---
Explanation:
Understanding Assertion (A):
- The given polynomial is x³-3x² + k.
- If x - 2 is a factor of this polynomial, it means that when x = 2, the polynomial should equal 0.
- Substituting x = 2 in the polynomial, we get: 2³ - 3(2)² + k = 0.
- Solving this equation gives us k = 4, which satisfies the condition for x - 2 to be a factor.
Understanding Reason (R):
- If x - a is a factor of a polynomial f(x), it implies that f(a) = 0.
- This is based on the factor theorem which states that if a polynomial f(x) is divided by x - a, the remainder is 0.
- Therefore, when x = a, the polynomial f(x) evaluates to 0, indicating that x - a is indeed a factor of f(x).
Conclusion:
- The given assertion is true because when k = 4, x - 2 becomes a factor of the polynomial x³-3x² + k.
- The reason provided is also valid as it explains the general concept behind factors of a polynomial based on the factor theorem.
- Hence, both the assertion and reason are correct, and the reason is the correct explanation for the assertion.
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In this question, a statement of Assertion (A) is followed by a statement of Reason (R).Assertion (A): The value of k for which x - 2 is a factor of x³-3x² + k is 4. 1Reason (R): If f(x) is a polynomial of degree greater than or equal to 1 and a is a real number, thenx - a is a factor of f(x) if f(a) = 0.?
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In this question, a statement of Assertion (A) is followed by a statement of Reason (R).Assertion (A): The value of k for which x - 2 is a factor of x³-3x² + k is 4. 1Reason (R): If f(x) is a polynomial of degree greater than or equal to 1 and a is a real number, thenx - a is a factor of f(x) if f(a) = 0.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In this question, a statement of Assertion (A) is followed by a statement of Reason (R).Assertion (A): The value of k for which x - 2 is a factor of x³-3x² + k is 4. 1Reason (R): If f(x) is a polynomial of degree greater than or equal to 1 and a is a real number, thenx - a is a factor of f(x) if f(a) = 0.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In this question, a statement of Assertion (A) is followed by a statement of Reason (R).Assertion (A): The value of k for which x - 2 is a factor of x³-3x² + k is 4. 1Reason (R): If f(x) is a polynomial of degree greater than or equal to 1 and a is a real number, thenx - a is a factor of f(x) if f(a) = 0.?.
In this question, a statement of Assertion (A) is followed by a statement of Reason (R).Assertion (A): The value of k for which x - 2 is a factor of x³-3x² + k is 4. 1Reason (R): If f(x) is a polynomial of degree greater than or equal to 1 and a is a real number, thenx - a is a factor of f(x) if f(a) = 0.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In this question, a statement of Assertion (A) is followed by a statement of Reason (R).Assertion (A): The value of k for which x - 2 is a factor of x³-3x² + k is 4. 1Reason (R): If f(x) is a polynomial of degree greater than or equal to 1 and a is a real number, thenx - a is a factor of f(x) if f(a) = 0.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In this question, a statement of Assertion (A) is followed by a statement of Reason (R).Assertion (A): The value of k for which x - 2 is a factor of x³-3x² + k is 4. 1Reason (R): If f(x) is a polynomial of degree greater than or equal to 1 and a is a real number, thenx - a is a factor of f(x) if f(a) = 0.?.
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