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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 both zeros of the quadratic polynomial x2 - 2kx + 2 are equal in magnitude but opposite in sign then value of k is 1/2.
Reason : Sum of zeros of a quadratic polynomial ax2 + bx + c is b/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 'D'. Can you explain this answer?
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Verified Answer
Direction: In the following questions, a statement of assertion (A) i...
As the polynomial is x2 - 2kx + 2 and its zeros are equal but opposition sign, sum of zeroes must be zero.
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sum of zeros = 0
Assertion (A) is false but reason (R) is true.
Thus (d) is correct option.
Most Upvoted Answer
Direction: In the following questions, a statement of assertion (A) i...
Assertion: If both zeros of the quadratic polynomial x^2 - 2kx + 2 are equal in magnitude but opposite in sign, then the value of k is 1/2.
Reason: The sum of the zeros of a quadratic polynomial ax^2 + bx + c is -b/a.
The correct answer is option D, Assertion (A) is false but reason (R) is true.
Explanation:
Let's solve the quadratic polynomial x^2 - 2kx + 2 to find its zeros.
The quadratic polynomial can be factored as (x - r)(x + r) = 0, where r is the magnitude of the zeros.
Expanding the equation, we get x^2 + rx - rx - r^2 = 0.
This simplifies to x^2 - r^2 = 0.
So, the zeros of the quadratic polynomial are x = ±r.
According to the given assertion, the zeros are equal in magnitude but opposite in sign. This means that r is a non-zero value.
Therefore, the zeros of the quadratic polynomial are x = r and x = -r.
Using the sum of zeros formula for the quadratic polynomial ax^2 + bx + c, we have:
Sum of zeros = -b/a
In this case, the sum of zeros is r + (-r) = 0.
Comparing this with the formula, we have -b/a = 0.
To satisfy this equation, b must be equal to 0.
However, in the original quadratic polynomial x^2 - 2kx + 2, the coefficient of x is -2k, not 0.
Therefore, the assertion is false.
However, the reason is true because the sum of zeros of any quadratic polynomial is given by -b/a.
Hence, the correct answer is option D: Assertion (A) is false but reason (R) is true.
Reason: The sum of the zeros of a quadratic polynomial ax^2 + bx + c is -b/a.
The correct answer is option D, Assertion (A) is false but reason (R) is true.
Explanation:
Let's solve the quadratic polynomial x^2 - 2kx + 2 to find its zeros.
The quadratic polynomial can be factored as (x - r)(x + r) = 0, where r is the magnitude of the zeros.
Expanding the equation, we get x^2 + rx - rx - r^2 = 0.
This simplifies to x^2 - r^2 = 0.
So, the zeros of the quadratic polynomial are x = ±r.
According to the given assertion, the zeros are equal in magnitude but opposite in sign. This means that r is a non-zero value.
Therefore, the zeros of the quadratic polynomial are x = r and x = -r.
Using the sum of zeros formula for the quadratic polynomial ax^2 + bx + c, we have:
Sum of zeros = -b/a
In this case, the sum of zeros is r + (-r) = 0.
Comparing this with the formula, we have -b/a = 0.
To satisfy this equation, b must be equal to 0.
However, in the original quadratic polynomial x^2 - 2kx + 2, the coefficient of x is -2k, not 0.
Therefore, the assertion is false.
However, the reason is true because the sum of zeros of any quadratic polynomial is given by -b/a.
Hence, 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 both zeros of the quadratic polynomial x2 - 2kx + 2 are equal in magnitude but opposite in sign then value of k is 1/2.Reason : Sum of zeros of a quadratic polynomial ax2 + bx + c is b/aa)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 both zeros of the quadratic polynomial x2 - 2kx + 2 are equal in magnitude but opposite in sign then value of k is 1/2.Reason : Sum of zeros of a quadratic polynomial ax2 + bx + c is b/aa)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 both zeros of the quadratic polynomial x2 - 2kx + 2 are equal in magnitude but opposite in sign then value of k is 1/2.Reason : Sum of zeros of a quadratic polynomial ax2 + bx + c is b/aa)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 both zeros of the quadratic polynomial x2 - 2kx + 2 are equal in magnitude but opposite in sign then value of k is 1/2.Reason : Sum of zeros of a quadratic polynomial ax2 + bx + c is b/aa)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 both zeros of the quadratic polynomial x2 - 2kx + 2 are equal in magnitude but opposite in sign then value of k is 1/2.Reason : Sum of zeros of a quadratic polynomial ax2 + bx + c is b/aa)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 both zeros of the quadratic polynomial x2 - 2kx + 2 are equal in magnitude but opposite in sign then value of k is 1/2.Reason : Sum of zeros of a quadratic polynomial ax2 + bx + c is b/aa)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 both zeros of the quadratic polynomial x2 - 2kx + 2 are equal in magnitude but opposite in sign then value of k is 1/2.Reason : Sum of zeros of a quadratic polynomial ax2 + bx + c is b/aa)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 both zeros of the quadratic polynomial x2 - 2kx + 2 are equal in magnitude but opposite in sign then value of k is 1/2.Reason : Sum of zeros of a quadratic polynomial ax2 + bx + c is b/aa)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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