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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 (x + 1) is a factor of f(x) = x2 + ax + 2, then a = - 3.
Reason : If (x - a) is a factor of p (x), if p (a) = 0.
- 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 'D'. Can you explain this answer?
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Direction: In the following questions, a statement of assertion (A) i...
If p (a) = 0, then x-a is a factor of that polynomial p(x). x - a would be the factor of the polynomial if the r(x) i.e. remainder is 0.
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Direction: In the following questions, a statement of assertion (A) i...
Assertion: If (x - 1) is a factor of f(x) = x^2 - ax + 2, then a = -3.
Reason: If (x - a) is a factor of p(x), then p(a) = 0.
The correct answer is option 'D' - Assertion (A) is false but reason (R) is true.
Explanation:
To determine if the assertion and reason are true or false, let's analyze each statement separately.
Assertion: If (x - 1) is a factor of f(x) = x^2 - ax + 2, then a = -3.
To check if (x - 1) is a factor of f(x), we can divide f(x) by (x - 1) and check if the remainder is zero.
Let's perform the division:
x - 2
-------------
x - 1 | x^2 - ax + 2
- (x^2 - x)
------------
-ax + 2
+ ax - 2
----------
0
Since the remainder is zero, we can conclude that (x - 1) is indeed a factor of f(x) = x^2 - ax + 2.
Now, let's analyze the assertion that a = -3. From the division above, we can see that the remainder is zero for any value of 'a'. Therefore, we cannot determine the value of 'a' based on the given information. Hence, the assertion is false.
Reason: If (x - a) is a factor of p(x), then p(a) = 0.
This reason is true based on the factor theorem. According to the factor theorem, if (x - a) is a factor of a polynomial function p(x), then p(a) = 0. This means that if we substitute the value of 'a' into the polynomial function, the result will be zero.
In the given context, the factor theorem implies that if (x - 1) is a factor of f(x) = x^2 - ax + 2, then f(1) = 0. Let's substitute x = 1 into f(x):
f(1) = 1^2 - a(1) + 2
= 1 - a + 2
= 3 - a
To satisfy the condition f(1) = 0, we must have 3 - a = 0, which implies a = 3. Therefore, the reason is true.
To summarize:
- The assertion that a = -3 is false.
- The reason that if (x - a) is a factor of p(x), then p(a) = 0 is true.
Therefore, the correct answer is option 'D' - Assertion (A) is false but reason (R) is true.
Reason: If (x - a) is a factor of p(x), then p(a) = 0.
The correct answer is option 'D' - Assertion (A) is false but reason (R) is true.
Explanation:
To determine if the assertion and reason are true or false, let's analyze each statement separately.
Assertion: If (x - 1) is a factor of f(x) = x^2 - ax + 2, then a = -3.
To check if (x - 1) is a factor of f(x), we can divide f(x) by (x - 1) and check if the remainder is zero.
Let's perform the division:
x - 2
-------------
x - 1 | x^2 - ax + 2
- (x^2 - x)
------------
-ax + 2
+ ax - 2
----------
0
Since the remainder is zero, we can conclude that (x - 1) is indeed a factor of f(x) = x^2 - ax + 2.
Now, let's analyze the assertion that a = -3. From the division above, we can see that the remainder is zero for any value of 'a'. Therefore, we cannot determine the value of 'a' based on the given information. Hence, the assertion is false.
Reason: If (x - a) is a factor of p(x), then p(a) = 0.
This reason is true based on the factor theorem. According to the factor theorem, if (x - a) is a factor of a polynomial function p(x), then p(a) = 0. This means that if we substitute the value of 'a' into the polynomial function, the result will be zero.
In the given context, the factor theorem implies that if (x - 1) is a factor of f(x) = x^2 - ax + 2, then f(1) = 0. Let's substitute x = 1 into f(x):
f(1) = 1^2 - a(1) + 2
= 1 - a + 2
= 3 - a
To satisfy the condition f(1) = 0, we must have 3 - a = 0, which implies a = 3. Therefore, the reason is true.
To summarize:
- The assertion that a = -3 is false.
- The reason that if (x - a) is a factor of p(x), then p(a) = 0 is true.
Therefore, the correct answer is option 'D' - Assertion (A) is false but reason (R) is true.
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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 (x + 1) is a factor of f(x) = x2 + ax + 2, then a = - 3.Reason : If (x - a) is a factor of p (x), if p (a) = 0.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 'D'. 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 (x + 1) is a factor of f(x) = x2 + ax + 2, then a = - 3.Reason : If (x - a) is a factor of p (x), if p (a) = 0.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 'D'. 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 (x + 1) is a factor of f(x) = x2 + ax + 2, then a = - 3.Reason : If (x - a) is a factor of p (x), if p (a) = 0.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 'D'. 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 (x + 1) is a factor of f(x) = x2 + ax + 2, then a = - 3.Reason : If (x - a) is a factor of p (x), if p (a) = 0.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 'D'. 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 (x + 1) is a factor of f(x) = x2 + ax + 2, then a = - 3.Reason : If (x - a) is a factor of p (x), if p (a) = 0.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 'D'. 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 (x + 1) is a factor of f(x) = x2 + ax + 2, then a = - 3.Reason : If (x - a) is a factor of p (x), if p (a) = 0.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 'D'. 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 (x + 1) is a factor of f(x) = x2 + ax + 2, then a = - 3.Reason : If (x - a) is a factor of p (x), if p (a) = 0.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 'D'. 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 (x + 1) is a factor of f(x) = x2 + ax + 2, then a = - 3.Reason : If (x - a) is a factor of p (x), if p (a) = 0.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 'D'. 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 (x + 1) is a factor of f(x) = x2 + ax + 2, then a = - 3.Reason : If (x - a) is a factor of p (x), if p (a) = 0.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 'D'. 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 (x + 1) is a factor of f(x) = x2 + ax + 2, then a = - 3.Reason : If (x - a) is a factor of p (x), if p (a) = 0.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 'D'. 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 (x + 1) is a factor of f(x) = x2 + ax + 2, then a = - 3.Reason : If (x - a) is a factor of p (x), if p (a) = 0.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 'D'. 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 (x + 1) is a factor of f(x) = x2 + ax + 2, then a = - 3.Reason : If (x - a) is a factor of p (x), if p (a) = 0.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 'D'. 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 (x + 1) is a factor of f(x) = x2 + ax + 2, then a = - 3.Reason : If (x - a) is a factor of p (x), if p (a) = 0.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 'D'. Can you explain this answer? tests, examples and also practice Class 9 tests.
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