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If p and q are the zeroes of the polynomial x2- 5x + k. Such that p - q = 1, find the value of K
- a)6
- b)7
- c)8
- d)9
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If p and q are the zeroes of the polynomial x2- 5x + k. Such that p - ...
Given α and β are the zeroes of the polynomial x2 − 5x + k
Also given that α − β = 1 → (1)
Recall that sum of roots (α + β) = −(b/a)
∴ α + β = 5 → (2)
Add (1) and (2), we get
α − β = 1
α + β = 5
2α = 6
∴ α = 3
Put α = 3 in α + β = 5
3 + β = 5
∴ β = 2
Hence 3 and 2 are zeroes of the given polynomial
Put x = 2 in the given polynomial to find the value of k ( Since 2 is a zero of the polynomial, f(2) will be 0 )
x2 − 5x + k = 0
⇒ 22 − 5(2) + k = 0
⇒ 4 − 10 + k = 0
⇒ − 6 + k = 0
∴ k = 6
Also given that α − β = 1 → (1)
Recall that sum of roots (α + β) = −(b/a)
∴ α + β = 5 → (2)
Add (1) and (2), we get
α − β = 1
α + β = 5
2α = 6
∴ α = 3
Put α = 3 in α + β = 5
3 + β = 5
∴ β = 2
Hence 3 and 2 are zeroes of the given polynomial
Put x = 2 in the given polynomial to find the value of k ( Since 2 is a zero of the polynomial, f(2) will be 0 )
x2 − 5x + k = 0
⇒ 22 − 5(2) + k = 0
⇒ 4 − 10 + k = 0
⇒ − 6 + k = 0
∴ k = 6
Most Upvoted Answer
If p and q are the zeroes of the polynomial x2- 5x + k. Such that p - ...
In the equation x² - 5x - k,
p + q = 5 and it is given that p - q = 1...
so, by solving, we get p = 3 and q = 2...
also, in this polynomial,...
pq = k ⇒ k = 3×2 = 6
p + q = 5 and it is given that p - q = 1...
so, by solving, we get p = 3 and q = 2...
also, in this polynomial,...
pq = k ⇒ k = 3×2 = 6
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Community Answer
If p and q are the zeroes of the polynomial x2- 5x + k. Such that p - ...
Given polynomial: x^2 - 5x - k
Let p and q be the zeroes of this polynomial.
We are given that p - q = 1
Using sum and product of zeroes formula:
p + q = 5
pq = -k
Finding the value of k using p and q:
(p - q)^2 = (p + q)^2 - 4pq
1 = 25 - 4(-k)
1 = 25 + 4k
4k = -24
k = -6
Therefore, the value of k is -6, which corresponds to option A.
Let p and q be the zeroes of this polynomial.
We are given that p - q = 1
Using sum and product of zeroes formula:
p + q = 5
pq = -k
Finding the value of k using p and q:
(p - q)^2 = (p + q)^2 - 4pq
1 = 25 - 4(-k)
1 = 25 + 4k
4k = -24
k = -6
Therefore, the value of k is -6, which corresponds to option A.
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If p and q are the zeroes of the polynomial x2- 5x + k. Such that p - q = 1, find the value of Ka)6b)7c)8d)9Correct 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 p and q are the zeroes of the polynomial x2- 5x + k. Such that p - q = 1, find the value of Ka)6b)7c)8d)9Correct 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 p and q are the zeroes of the polynomial x2- 5x + k. Such that p - q = 1, find the value of Ka)6b)7c)8d)9Correct answer is option 'A'. Can you explain this answer?.
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