Class 10 Exam > Class 10 Questions > If one of the zeroes of cubic polynomial x3+ ...
Start Learning for Free
If one of the zeroes of cubic polynomial x3+ px2+ q+
r is - 1, then the product of the other two zeroes is a) p q 1 b) p-q-1 c) q-p 1 d) q-p-1?
r is - 1, then the product of the other two zeroes is a) p q 1 b) p-q-1 c) q-p 1 d) q-p-1?
Most Upvoted Answer
If one of the zeroes of cubic polynomial x3+ px2+ q+r is - 1, then the...
Community Answer
If one of the zeroes of cubic polynomial x3+ px2+ q+r is - 1, then the...
Explanation:
A cubic polynomial is of the form ax^3 + bx^2 + cx + d where a, b, c, and d are constants.
Let α, β, and γ be the zeroes of the cubic polynomial x^3 + px^2 + qx + r. Then, by the factor theorem, we have:
- x^3 + px^2 + qx + r = (x - α)(x - β)(x - γ)
Given that one of the zeroes is -1, we can substitute this value in the equation above to get:
- 1 - p + q + r = 0
Therefore, we have:
- p - q - r = 1
Let the other two zeroes be α and β. Then, by Vieta's formulas, we have:
- αβγ = -r
- α + β + γ = -p
- αβ + βγ + γα = q
Since one of the zeroes is -1, we can rewrite the above equations as:
- αβ = -r/γ
- α + β + γ = -p
- αβ + βγ + γα = q
- αβγ = -r
- αβγ = γ(-r/γ) = -rγ
- αβ + βγ + γα = αβ + γ(-1) + α(-1) = αβ - γ - α
Substituting the values of αβγ and αβ + βγ + γα in the equation αβγ = -r, we get:
- (αβ - γ - α)γ = -r
- αβγ - γ^2 - αγ = -r
- -r - γ^2 - αγ = -r
- γ^2 + αγ = 0
- γ(γ + α) = 0
Since γ = -1, we have:
- αβ - γ - α = αβ + 1 + α = α(α + β + 1) = -r/γ = r
Substituting α + β = -γ - p = 1 - p and simplifying, we get:
- αβ = r - α - β = r - (1 - p) = p - r + 1
Therefore, the product of the other two zeroes is p - r + 1.
Hence, the answer is option (d) q - p - 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
If one of the zeroes of cubic polynomial x3+ px2+ q+r is - 1, then the product of the other two zeroes is a) p q 1 b) p-q-1 c) q-p 1 d) q-p-1?
Question Description
If one of the zeroes of cubic polynomial x3+ px2+ q+r is - 1, then the product of the other two zeroes is a) p q 1 b) p-q-1 c) q-p 1 d) q-p-1? 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 If one of the zeroes of cubic polynomial x3+ px2+ q+r is - 1, then the product of the other two zeroes is a) p q 1 b) p-q-1 c) q-p 1 d) q-p-1? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one of the zeroes of cubic polynomial x3+ px2+ q+r is - 1, then the product of the other two zeroes is a) p q 1 b) p-q-1 c) q-p 1 d) q-p-1?.
If one of the zeroes of cubic polynomial x3+ px2+ q+r is - 1, then the product of the other two zeroes is a) p q 1 b) p-q-1 c) q-p 1 d) q-p-1? 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 If one of the zeroes of cubic polynomial x3+ px2+ q+r is - 1, then the product of the other two zeroes is a) p q 1 b) p-q-1 c) q-p 1 d) q-p-1? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one of the zeroes of cubic polynomial x3+ px2+ q+r is - 1, then the product of the other two zeroes is a) p q 1 b) p-q-1 c) q-p 1 d) q-p-1?.
Solutions for If one of the zeroes of cubic polynomial x3+ px2+ q+r is - 1, then the product of the other two zeroes is a) p q 1 b) p-q-1 c) q-p 1 d) q-p-1? 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 If one of the zeroes of cubic polynomial x3+ px2+ q+r is - 1, then the product of the other two zeroes is a) p q 1 b) p-q-1 c) q-p 1 d) q-p-1? defined & explained in the simplest way possible. Besides giving the explanation of
If one of the zeroes of cubic polynomial x3+ px2+ q+r is - 1, then the product of the other two zeroes is a) p q 1 b) p-q-1 c) q-p 1 d) q-p-1?, a detailed solution for If one of the zeroes of cubic polynomial x3+ px2+ q+r is - 1, then the product of the other two zeroes is a) p q 1 b) p-q-1 c) q-p 1 d) q-p-1? has been provided alongside types of If one of the zeroes of cubic polynomial x3+ px2+ q+r is - 1, then the product of the other two zeroes is a) p q 1 b) p-q-1 c) q-p 1 d) q-p-1? theory, EduRev gives you an
ample number of questions to practice If one of the zeroes of cubic polynomial x3+ px2+ q+r is - 1, then the product of the other two zeroes is a) p q 1 b) p-q-1 c) q-p 1 d) q-p-1? 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup