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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
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⇒ 2k = 0 & k = 0
So, A is incorrect but R is correct.
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Direction: In the following questions, a statement of assertion (A) i...
Assertion and Reasoning
Assertion: If both zeros of the quadratic polynomial x2 - 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 ax2 + bx + c is -b/a.
Explanation:
- A quadratic polynomial is of the form ax2 + bx + c, where a, b, and c are constants.
- The zeros of a quadratic polynomial are the values of x for which the polynomial is equal to zero.
- If both zeros of the quadratic polynomial x2 - 2kx + 2 are equal in magnitude but opposite in sign, then the quadratic polynomial can be written as (x + a)(x - a), where a is a positive constant. This is because the product of two factors with opposite signs is negative, and the sum of the factors is zero.
- Expanding (x + a)(x - a) gives x2 - a2. Therefore, x2 - 2kx + 2 can be written as x2 - a2 + 2a - 2a - 2kx = (x - a)(x + a) - 2kx = 0.
- The sum of the zeros of the quadratic polynomial x2 - 2kx + 2 is equal to the negative of the coefficient of x divided by the coefficient of x2. Therefore, the sum of the zeros is -(-2k)/1 = 2k.
- If both zeros of the quadratic polynomial x2 - 2kx + 2 are equal in magnitude but opposite in sign, then the sum of the zeros is zero. Therefore, 2k = 0, which implies k = 0/2 = 0.5 or 1/2.
Conclusion:
- The assertion is false because the value of k can be either 0.5 or 1/2.
- The reasoning is true because the sum of the zeros of a quadratic polynomial ax2 + bx + c is -b/a.
Assertion: If both zeros of the quadratic polynomial x2 - 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 ax2 + bx + c is -b/a.
Explanation:
- A quadratic polynomial is of the form ax2 + bx + c, where a, b, and c are constants.
- The zeros of a quadratic polynomial are the values of x for which the polynomial is equal to zero.
- If both zeros of the quadratic polynomial x2 - 2kx + 2 are equal in magnitude but opposite in sign, then the quadratic polynomial can be written as (x + a)(x - a), where a is a positive constant. This is because the product of two factors with opposite signs is negative, and the sum of the factors is zero.
- Expanding (x + a)(x - a) gives x2 - a2. Therefore, x2 - 2kx + 2 can be written as x2 - a2 + 2a - 2a - 2kx = (x - a)(x + a) - 2kx = 0.
- The sum of the zeros of the quadratic polynomial x2 - 2kx + 2 is equal to the negative of the coefficient of x divided by the coefficient of x2. Therefore, the sum of the zeros is -(-2k)/1 = 2k.
- If both zeros of the quadratic polynomial x2 - 2kx + 2 are equal in magnitude but opposite in sign, then the sum of the zeros is zero. Therefore, 2k = 0, which implies k = 0/2 = 0.5 or 1/2.
Conclusion:
- The assertion is false because the value of k can be either 0.5 or 1/2.
- The reasoning is true because the sum of the zeros of a quadratic polynomial ax2 + bx + c is -b/a.
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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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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? 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/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? 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/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?.
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? 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/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? 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/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?.
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/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? 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 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? defined & explained in the simplest way possible. Besides giving the explanation of
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