Quant Exam > Quant Questions > If the quadratic equation kx(x – 2) + 6...
Start Learning for Free
If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ is
- a)5
- b)4
- c)3
- d)6
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, the...
Most Upvoted Answer
If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, the...
Solution:
Given quadratic equation:
kx(x + 2) + 6 = 0
To find the value of k:
Let's solve the quadratic equation and find the value of k.
Step 1: Rewrite the quadratic equation in standard form:
kx^2 + 2kx + 6 = 0
Step 2: Calculate the discriminant:
The discriminant (D) of a quadratic equation is given by the formula:
D = b^2 - 4ac
In our equation, a = k, b = 2k, and c = 6.
Substituting the values, we get:
D = (2k)^2 - 4(k)(6)
D = 4k^2 - 24k
Step 3: Determine the condition for equal roots:
For a quadratic equation to have equal roots, the discriminant should be equal to zero.
So, D = 0.
Step 4: Solve the equation D = 0:
4k^2 - 24k = 0
Dividing the equation by 4:
k^2 - 6k = 0
Factoring out k:
k(k - 6) = 0
Step 5: Find the values of k:
Setting each factor equal to zero:
k = 0 or k - 6 = 0
Solving for k:
k = 0 or k = 6
Conclusion:
The values of k that satisfy the condition for equal roots are k = 0 and k = 6.
However, the given options are a) 5, b) 4, c) 3, and d) 6.
Therefore, the correct answer is option 'D' (6).
Given quadratic equation:
kx(x + 2) + 6 = 0
To find the value of k:
Let's solve the quadratic equation and find the value of k.
Step 1: Rewrite the quadratic equation in standard form:
kx^2 + 2kx + 6 = 0
Step 2: Calculate the discriminant:
The discriminant (D) of a quadratic equation is given by the formula:
D = b^2 - 4ac
In our equation, a = k, b = 2k, and c = 6.
Substituting the values, we get:
D = (2k)^2 - 4(k)(6)
D = 4k^2 - 24k
Step 3: Determine the condition for equal roots:
For a quadratic equation to have equal roots, the discriminant should be equal to zero.
So, D = 0.
Step 4: Solve the equation D = 0:
4k^2 - 24k = 0
Dividing the equation by 4:
k^2 - 6k = 0
Factoring out k:
k(k - 6) = 0
Step 5: Find the values of k:
Setting each factor equal to zero:
k = 0 or k - 6 = 0
Solving for k:
k = 0 or k = 6
Conclusion:
The values of k that satisfy the condition for equal roots are k = 0 and k = 6.
However, the given options are a) 5, b) 4, c) 3, and d) 6.
Therefore, the correct answer is option 'D' (6).
|
Explore Courses for Quant exam
|
|
If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer?
Question Description
If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer?.
If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer?.
Solutions for If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer?, a detailed solution for If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup