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Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : If f(x) = x4 + x3 - 2x2 + x + 1 is divided by (x - 1), then its remainder is 2.
Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a , then the remainder is p(-a).
- a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Assertion (A) is true but reason (R) is false.
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'C'. Can you explain this answer?
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Direction: In the following questions, a statement of assertion (A) i...
According to remainder theorem: Let p(x) be any polynomial of degree greater than or equal to one and is divided by the linear polynomial x - a where a be any number which would be the divisor and we get the value of x = a, then the remainder is p (-a). Factor theorem is a special case for the remainder theorem.
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Direction: In the following questions, a statement of assertion (A) i...
Assertion (A): If f(x) = x^4 - x^3 - 2x^2 - x + 1 is divided by (x - 1), then its remainder is 2.
Reason (R): If p(x) is a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a, then the remainder is p(-a).
To determine whether the given assertion and reason are true or false, let's analyze each statement separately.
Assertion (A)
To find the remainder when f(x) is divided by (x - 1), we can use synthetic division or long division.
Using synthetic division:
1 | 1 -1 -2 -1 1
| 1 0 -2 -3
+------------------
1 0 -2 -3 -2
The remainder when f(x) is divided by (x - 1) is -2. Therefore, the assertion (A) is false.
Reason (R)
The reason states that if p(x) is a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a, then the remainder is p(-a).
This statement is true. When a polynomial of degree greater than or equal to one is divided by a linear polynomial, the remainder is equal to the value of the polynomial at the point x = a. In other words, substituting x = -a into the polynomial will give the remainder.
Since the reason (R) is true, but the assertion (A) is false, the correct answer is (C) Assertion (A) is true but reason (R) is false.
Reason (R): If p(x) is a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a, then the remainder is p(-a).
To determine whether the given assertion and reason are true or false, let's analyze each statement separately.
Assertion (A)
To find the remainder when f(x) is divided by (x - 1), we can use synthetic division or long division.
Using synthetic division:
1 | 1 -1 -2 -1 1
| 1 0 -2 -3
+------------------
1 0 -2 -3 -2
The remainder when f(x) is divided by (x - 1) is -2. Therefore, the assertion (A) is false.
Reason (R)
The reason states that if p(x) is a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a, then the remainder is p(-a).
This statement is true. When a polynomial of degree greater than or equal to one is divided by a linear polynomial, the remainder is equal to the value of the polynomial at the point x = a. In other words, substituting x = -a into the polynomial will give the remainder.
Since the reason (R) is true, but the assertion (A) is false, the correct answer is (C) Assertion (A) is true but reason (R) is false.
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Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If f(x) = x4 + x3 - 2x2 + x + 1 is divided by (x - 1), then its remainder is 2.Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a , then the remainder is p(-a).a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer?
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Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If f(x) = x4 + x3 - 2x2 + x + 1 is divided by (x - 1), then its remainder is 2.Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a , then the remainder is p(-a).a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If f(x) = x4 + x3 - 2x2 + x + 1 is divided by (x - 1), then its remainder is 2.Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a , then the remainder is p(-a).a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If f(x) = x4 + x3 - 2x2 + x + 1 is divided by (x - 1), then its remainder is 2.Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a , then the remainder is p(-a).a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer?.
Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If f(x) = x4 + x3 - 2x2 + x + 1 is divided by (x - 1), then its remainder is 2.Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a , then the remainder is p(-a).a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If f(x) = x4 + x3 - 2x2 + x + 1 is divided by (x - 1), then its remainder is 2.Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a , then the remainder is p(-a).a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If f(x) = x4 + x3 - 2x2 + x + 1 is divided by (x - 1), then its remainder is 2.Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a , then the remainder is p(-a).a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer?.
Solutions for Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If f(x) = x4 + x3 - 2x2 + x + 1 is divided by (x - 1), then its remainder is 2.Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a , then the remainder is p(-a).a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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Here you can find the meaning of Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If f(x) = x4 + x3 - 2x2 + x + 1 is divided by (x - 1), then its remainder is 2.Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a , then the remainder is p(-a).a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If f(x) = x4 + x3 - 2x2 + x + 1 is divided by (x - 1), then its remainder is 2.Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a , then the remainder is p(-a).a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If f(x) = x4 + x3 - 2x2 + x + 1 is divided by (x - 1), then its remainder is 2.Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a , then the remainder is p(-a).a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If f(x) = x4 + x3 - 2x2 + x + 1 is divided by (x - 1), then its remainder is 2.Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a , then the remainder is p(-a).a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If f(x) = x4 + x3 - 2x2 + x + 1 is divided by (x - 1), then its remainder is 2.Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x - a , then the remainder is p(-a).a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 9 tests.
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