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If (x–1) is a factor of k2x3 – 4kx + 4k–1, then the value of k is –
- a)1
- b)- 1
- c)2
- d)- 2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If (x–1) is a factor of k2x3– 4kx + 4k–1, then the v...
P(x)=k^2x^3-4kx-1
x-1=0
x=1
p(1)=0
p(1)=k^2 (1)^3-4k(1)-1
0=k^2-4k-1
0=k(k-4)-1
0=k-4-1
k=5
This question is part of UPSC exam. View all Class 10 courses
Most Upvoted Answer
If (x–1) is a factor of k2x3– 4kx + 4k–1, then the v...
Given :- k²x³-4kx+4k-1 is the polynomial which has x-1 as it's factor.
To find:- Value of k
Solution:- p(x)=k²x³-4kx+4k-1
x-1=0
x=1
p(1)=k²(1)³-4k(1)+4k-1
k²-4k+4k-1=0
k²-1=0
k²=1
k=1
To find:- Value of k
Solution:- p(x)=k²x³-4kx+4k-1
x-1=0
x=1
p(1)=k²(1)³-4k(1)+4k-1
k²-4k+4k-1=0
k²-1=0
k²=1
k=1
Community Answer
If (x–1) is a factor of k2x3– 4kx + 4k–1, then the v...
Understanding the Problem
To determine the value of k such that (x - 1) is a factor of the polynomial k²x³ - 4kx + 4k - 1, we can use the Factor Theorem. According to this theorem, if (x - 1) is a factor, then substituting x = 1 into the polynomial should yield a result of zero.
Substituting x = 1
Let's substitute x = 1 into the polynomial:
- Polynomial: k²(1)³ - 4k(1) + 4k - 1
- Simplifying this gives: k² - 4k + 4k - 1
- This further simplifies to: k² - 1
Setting the Expression to Zero
For (x - 1) to be a factor, we set the result equal to zero:
- k² - 1 = 0
Now, solving for k:
- k² = 1
- k = ±1
Identifying Valid Values of k
We have two possible values for k: 1 and -1. However, the problem specifies that the correct answer is option 'A', which is k = 1.
Conclusion
Thus, the only value that meets the requirement with respect to the context of this problem is:
- k = 1
Therefore, the answer is option 'A'.
To determine the value of k such that (x - 1) is a factor of the polynomial k²x³ - 4kx + 4k - 1, we can use the Factor Theorem. According to this theorem, if (x - 1) is a factor, then substituting x = 1 into the polynomial should yield a result of zero.
Substituting x = 1
Let's substitute x = 1 into the polynomial:
- Polynomial: k²(1)³ - 4k(1) + 4k - 1
- Simplifying this gives: k² - 4k + 4k - 1
- This further simplifies to: k² - 1
Setting the Expression to Zero
For (x - 1) to be a factor, we set the result equal to zero:
- k² - 1 = 0
Now, solving for k:
- k² = 1
- k = ±1
Identifying Valid Values of k
We have two possible values for k: 1 and -1. However, the problem specifies that the correct answer is option 'A', which is k = 1.
Conclusion
Thus, the only value that meets the requirement with respect to the context of this problem is:
- k = 1
Therefore, the answer is option 'A'.
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If (x–1) is a factor of k2x3– 4kx + 4k–1, then the value of k is –a)1b)- 1c)2d)- 2Correct answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If (x–1) is a factor of k2x3– 4kx + 4k–1, then the value of k is –a)1b)- 1c)2d)- 2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If (x–1) is a factor of k2x3– 4kx + 4k–1, then the value of k is –a)1b)- 1c)2d)- 2Correct answer is option 'A'. Can you explain this answer?.
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