Class 10 Exam > Class 10 Questions > DIRECTION : In the following questions, a st...
Start Learning for Free
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : The value of k = 2 , if one root of the quadratic equation 6x2 -x- k = 0 is ⅔
Reason : The quadratic equation ax2 + bx + c = 0, a ≠ 0 a has two roots.
- 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 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
DIRECTION : In the following questions, a statement of assertion (A) ...
As one root is 
x = 
x = 
k = 2
So, both A and R are correct but R does not explain A.
Most Upvoted Answer
DIRECTION : In the following questions, a statement of assertion (A) ...
Answer:
Assertion (A): The value of k = 2, if one root of the quadratic equation 6x^2 - x - k = 0 is 2/3.
Reason (R): The quadratic equation ax^2 + bx + c = 0, where a ≠ 0, has two roots.
Explanation:
To determine the validity of the assertion and reason, let's analyze the given quadratic equation and its roots.
The given quadratic equation is 6x^2 - x - k = 0.
We know that a quadratic equation of the form ax^2 + bx + c = 0 has two roots, which can be determined using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Comparing this with the given equation, we have a = 6, b = -1, and c = -k.
Now, let's substitute these values into the quadratic formula and solve for x.
x = (-(-1) ± √((-1)^2 - 4(6)(-k))) / (2(6))
x = (1 ± √(1 + 24k)) / 12
According to the given information, one root of the quadratic equation is 2/3. Let's substitute this value into the equation:
2/3 = (1 ± √(1 + 24k)) / 12
Multiplying both sides of the equation by 12, we get:
8 = 1 ± √(1 + 24k)
Squaring both sides of the equation, we have:
64 = 1 ± 2√(1 + 24k) + 1 + 24k
64 = 2 ± 2√(1 + 24k) + 24k
Simplifying the equation, we get:
62 = ± 2√(1 + 24k) + 24k
Now, let's analyze the possible cases:
Case 1: Positive sign ( + ) in the equation
62 = 2√(1 + 24k) + 24k
62 - 24k = 2√(1 + 24k)
Squaring both sides of the equation, we have:
(62 - 24k)^2 = 4(1 + 24k)
3844 - 2976k + 576k^2 = 4 + 96k
576k^2 - 3072k + 3840 = 0
Dividing the equation by 64, we get:
9k^2 - 48k + 60 = 0
Factoring the quadratic equation, we have:
(3k - 10)(3k - 4) = 0
This gives two possible values for k: k = 10/3 or k = 4/3.
Case 2: Negative sign ( - ) in the equation
62 = -2√(1 + 24k) + 24k
62 - 24k = -2√(1 + 24k)
Squaring both sides of the equation, we have:
(62 - 24k)^2 = 4(1 +
Assertion (A): The value of k = 2, if one root of the quadratic equation 6x^2 - x - k = 0 is 2/3.
Reason (R): The quadratic equation ax^2 + bx + c = 0, where a ≠ 0, has two roots.
Explanation:
To determine the validity of the assertion and reason, let's analyze the given quadratic equation and its roots.
The given quadratic equation is 6x^2 - x - k = 0.
We know that a quadratic equation of the form ax^2 + bx + c = 0 has two roots, which can be determined using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Comparing this with the given equation, we have a = 6, b = -1, and c = -k.
Now, let's substitute these values into the quadratic formula and solve for x.
x = (-(-1) ± √((-1)^2 - 4(6)(-k))) / (2(6))
x = (1 ± √(1 + 24k)) / 12
According to the given information, one root of the quadratic equation is 2/3. Let's substitute this value into the equation:
2/3 = (1 ± √(1 + 24k)) / 12
Multiplying both sides of the equation by 12, we get:
8 = 1 ± √(1 + 24k)
Squaring both sides of the equation, we have:
64 = 1 ± 2√(1 + 24k) + 1 + 24k
64 = 2 ± 2√(1 + 24k) + 24k
Simplifying the equation, we get:
62 = ± 2√(1 + 24k) + 24k
Now, let's analyze the possible cases:
Case 1: Positive sign ( + ) in the equation
62 = 2√(1 + 24k) + 24k
62 - 24k = 2√(1 + 24k)
Squaring both sides of the equation, we have:
(62 - 24k)^2 = 4(1 + 24k)
3844 - 2976k + 576k^2 = 4 + 96k
576k^2 - 3072k + 3840 = 0
Dividing the equation by 64, we get:
9k^2 - 48k + 60 = 0
Factoring the quadratic equation, we have:
(3k - 10)(3k - 4) = 0
This gives two possible values for k: k = 10/3 or k = 4/3.
Case 2: Negative sign ( - ) in the equation
62 = -2√(1 + 24k) + 24k
62 - 24k = -2√(1 + 24k)
Squaring both sides of the equation, we have:
(62 - 24k)^2 = 4(1 +
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : The value of k = 2 , if one root of the quadratic equation 6x2 -x- k = 0 is ⅔Reason : The quadratic equation ax2 + bx + c = 0, a ≠ 0 a has two roots.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 'B'. Can you explain this answer?
Question Description
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : The value of k = 2 , if one root of the quadratic equation 6x2 -x- k = 0 is ⅔Reason : The quadratic equation ax2 + bx + c = 0, a ≠ 0 a has two roots.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 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 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 : The value of k = 2 , if one root of the quadratic equation 6x2 -x- k = 0 is ⅔Reason : The quadratic equation ax2 + bx + c = 0, a ≠ 0 a has two roots.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 'B'. Can you explain this answer? covers all topics & solutions for Class 10 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 : The value of k = 2 , if one root of the quadratic equation 6x2 -x- k = 0 is ⅔Reason : The quadratic equation ax2 + bx + c = 0, a ≠ 0 a has two roots.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 'B'. 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 : The value of k = 2 , if one root of the quadratic equation 6x2 -x- k = 0 is ⅔Reason : The quadratic equation ax2 + bx + c = 0, a ≠ 0 a has two roots.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 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 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 : The value of k = 2 , if one root of the quadratic equation 6x2 -x- k = 0 is ⅔Reason : The quadratic equation ax2 + bx + c = 0, a ≠ 0 a has two roots.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 'B'. Can you explain this answer? covers all topics & solutions for Class 10 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 : The value of k = 2 , if one root of the quadratic equation 6x2 -x- k = 0 is ⅔Reason : The quadratic equation ax2 + bx + c = 0, a ≠ 0 a has two roots.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 'B'. 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 : The value of k = 2 , if one root of the quadratic equation 6x2 -x- k = 0 is ⅔Reason : The quadratic equation ax2 + bx + c = 0, a ≠ 0 a has two roots.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 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
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 : The value of k = 2 , if one root of the quadratic equation 6x2 -x- k = 0 is ⅔Reason : The quadratic equation ax2 + bx + c = 0, a ≠ 0 a has two roots.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 'B'. 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 : The value of k = 2 , if one root of the quadratic equation 6x2 -x- k = 0 is ⅔Reason : The quadratic equation ax2 + bx + c = 0, a ≠ 0 a has two roots.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 'B'. 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 : The value of k = 2 , if one root of the quadratic equation 6x2 -x- k = 0 is ⅔Reason : The quadratic equation ax2 + bx + c = 0, a ≠ 0 a has two roots.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 'B'. 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 : The value of k = 2 , if one root of the quadratic equation 6x2 -x- k = 0 is ⅔Reason : The quadratic equation ax2 + bx + c = 0, a ≠ 0 a has two roots.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 'B'. 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 : The value of k = 2 , if one root of the quadratic equation 6x2 -x- k = 0 is ⅔Reason : The quadratic equation ax2 + bx + c = 0, a ≠ 0 a has two roots.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 'B'. Can you explain this answer? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup