Class 10 Exam > Class 10 Questions > Find the non - zero value of value of 𝑘, for...
Start Learning for Free
Find the non - zero value of value of 𝑘, for which the quadratic equation
𝑘𝑥
2 + 1 − 2(𝑘 − 1)𝑥 + 𝑥
2 = 0 has equal roots. Hence find the roots of the equation.?
𝑘𝑥
2 + 1 − 2(𝑘 − 1)𝑥 + 𝑥
2 = 0 has equal roots. Hence find the roots of the equation.?
Most Upvoted Answer
Find the non - zero value of value of 𝑘, for which the quadratic equa...
- **Finding the value of k for equal roots:**
Given quadratic equation: 𝑘𝑥^2 + 1 - 2(𝑘 - 1)𝑥 + 𝑥^2 = 0
For equal roots, the discriminant should be zero.
Discriminant = b^2 - 4ac = (-2(k-1))^2 - 4(k)(1) = 0
Solving this equation will give the value of k.
- **Solving for k:**
(-2(k-1))^2 - 4(k)(1) = 0
=> 4(k^2 - 2k + 1) - 4k = 0
=> 4k^2 - 8k + 4 - 4k = 0
=> 4k^2 - 12k + 4 = 0
=> k^2 - 3k + 1 = 0
Solving this quadratic equation will give the value of k.
- **Finding the roots of the equation:**
Substitute the value of k in the given quadratic equation and solve for x to find the roots.
Once you find the value of k, substitute it back into the equation 𝑘𝑥^2 + 1 - 2(𝑘 - 1)𝑥 + 𝑥^2 = 0 to get a simplified quadratic equation in terms of x.
Solve this quadratic equation to find the roots of the given equation.
By following these steps, you can determine the non-zero value of k for which the quadratic equation has equal roots and find those roots.
Given quadratic equation: 𝑘𝑥^2 + 1 - 2(𝑘 - 1)𝑥 + 𝑥^2 = 0
For equal roots, the discriminant should be zero.
Discriminant = b^2 - 4ac = (-2(k-1))^2 - 4(k)(1) = 0
Solving this equation will give the value of k.
- **Solving for k:**
(-2(k-1))^2 - 4(k)(1) = 0
=> 4(k^2 - 2k + 1) - 4k = 0
=> 4k^2 - 8k + 4 - 4k = 0
=> 4k^2 - 12k + 4 = 0
=> k^2 - 3k + 1 = 0
Solving this quadratic equation will give the value of k.
- **Finding the roots of the equation:**
Substitute the value of k in the given quadratic equation and solve for x to find the roots.
Once you find the value of k, substitute it back into the equation 𝑘𝑥^2 + 1 - 2(𝑘 - 1)𝑥 + 𝑥^2 = 0 to get a simplified quadratic equation in terms of x.
Solve this quadratic equation to find the roots of the given equation.
By following these steps, you can determine the non-zero value of k for which the quadratic equation has equal roots and find those roots.
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
Find the non - zero value of value of 𝑘, for which the quadratic equation 𝑘𝑥 2 + 1 − 2(𝑘 − 1)𝑥 + 𝑥 2 = 0 has equal roots. Hence find the roots of the equation.?
Question Description
Find the non - zero value of value of 𝑘, for which the quadratic equation 𝑘𝑥 2 + 1 − 2(𝑘 − 1)𝑥 + 𝑥 2 = 0 has equal roots. Hence find the roots of the equation.? 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 Find the non - zero value of value of 𝑘, for which the quadratic equation 𝑘𝑥 2 + 1 − 2(𝑘 − 1)𝑥 + 𝑥 2 = 0 has equal roots. Hence find the roots of the equation.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the non - zero value of value of 𝑘, for which the quadratic equation 𝑘𝑥 2 + 1 − 2(𝑘 − 1)𝑥 + 𝑥 2 = 0 has equal roots. Hence find the roots of the equation.?.
Find the non - zero value of value of 𝑘, for which the quadratic equation 𝑘𝑥 2 + 1 − 2(𝑘 − 1)𝑥 + 𝑥 2 = 0 has equal roots. Hence find the roots of the equation.? 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 Find the non - zero value of value of 𝑘, for which the quadratic equation 𝑘𝑥 2 + 1 − 2(𝑘 − 1)𝑥 + 𝑥 2 = 0 has equal roots. Hence find the roots of the equation.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the non - zero value of value of 𝑘, for which the quadratic equation 𝑘𝑥 2 + 1 − 2(𝑘 − 1)𝑥 + 𝑥 2 = 0 has equal roots. Hence find the roots of the equation.?.
Solutions for Find the non - zero value of value of 𝑘, for which the quadratic equation 𝑘𝑥 2 + 1 − 2(𝑘 − 1)𝑥 + 𝑥 2 = 0 has equal roots. Hence find the roots of the equation.? 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 Find the non - zero value of value of 𝑘, for which the quadratic equation 𝑘𝑥 2 + 1 − 2(𝑘 − 1)𝑥 + 𝑥 2 = 0 has equal roots. Hence find the roots of the equation.? defined & explained in the simplest way possible. Besides giving the explanation of
Find the non - zero value of value of 𝑘, for which the quadratic equation 𝑘𝑥 2 + 1 − 2(𝑘 − 1)𝑥 + 𝑥 2 = 0 has equal roots. Hence find the roots of the equation.?, a detailed solution for Find the non - zero value of value of 𝑘, for which the quadratic equation 𝑘𝑥 2 + 1 − 2(𝑘 − 1)𝑥 + 𝑥 2 = 0 has equal roots. Hence find the roots of the equation.? has been provided alongside types of Find the non - zero value of value of 𝑘, for which the quadratic equation 𝑘𝑥 2 + 1 − 2(𝑘 − 1)𝑥 + 𝑥 2 = 0 has equal roots. Hence find the roots of the equation.? theory, EduRev gives you an
ample number of questions to practice Find the non - zero value of value of 𝑘, for which the quadratic equation 𝑘𝑥 2 + 1 − 2(𝑘 − 1)𝑥 + 𝑥 2 = 0 has equal roots. Hence find the roots of the equation.? 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