Class 10 Exam > Class 10 Questions > If alpha ^ 2 * beta and alpha * beta ^ 2 are ...
Start Learning for Free
If alpha ^ 2 * beta and alpha * beta ^ 2 are zeroes of the polynomial x ^ 2 + px + q where a, beta are zeroes of polynomial 3x ^ 2 - x + 6 then find the values of p and q.?
Most Upvoted Answer
If alpha ^ 2 * beta and alpha * beta ^ 2 are zeroes of the polynomial ...
Given Information:
- Zeroes of the polynomial 3x^2 - x + 6 are alpha and beta.
- Zeroes of the polynomial x^2 + px + q are alpha^2 * beta and alpha * beta^2.
Finding p and q:
Step 1: Finding the Sum and Product of Zeroes of 3x^2 - x + 6:
- Sum of zeroes = -(-1)/3 = 1/3
- Product of zeroes = 6/3 = 2
Step 2: Using Sum and Product of Zeroes to find p and q:
- Sum of zeroes of x^2 + px + q = -p
- Product of zeroes of x^2 + px + q = q
Step 3: Finding p and q using the given information:
- Sum of zeroes of x^2 + px + q = alpha^2 * beta + alpha * beta^2 = alpha * beta (alpha + beta) = 1/3
- Product of zeroes of x^2 + px + q = alpha^2 * beta * alpha * beta^2 = (alpha * beta)^3 = 2
Step 4: Solving the Equations:
- From the first equation: alpha * beta = 1/3
- From the second equation: (alpha * beta)^3 = 2
-> (1/3)^3 = 2
-> 1/27 = 2
This is not possible, so there might be an error in the given information.
Conclusion:
- The values of p and q cannot be determined with the given information, as there seems to be an inconsistency in the conditions provided.
- Zeroes of the polynomial 3x^2 - x + 6 are alpha and beta.
- Zeroes of the polynomial x^2 + px + q are alpha^2 * beta and alpha * beta^2.
Finding p and q:
Step 1: Finding the Sum and Product of Zeroes of 3x^2 - x + 6:
- Sum of zeroes = -(-1)/3 = 1/3
- Product of zeroes = 6/3 = 2
Step 2: Using Sum and Product of Zeroes to find p and q:
- Sum of zeroes of x^2 + px + q = -p
- Product of zeroes of x^2 + px + q = q
Step 3: Finding p and q using the given information:
- Sum of zeroes of x^2 + px + q = alpha^2 * beta + alpha * beta^2 = alpha * beta (alpha + beta) = 1/3
- Product of zeroes of x^2 + px + q = alpha^2 * beta * alpha * beta^2 = (alpha * beta)^3 = 2
Step 4: Solving the Equations:
- From the first equation: alpha * beta = 1/3
- From the second equation: (alpha * beta)^3 = 2
-> (1/3)^3 = 2
-> 1/27 = 2
This is not possible, so there might be an error in the given information.
Conclusion:
- The values of p and q cannot be determined with the given information, as there seems to be an inconsistency in the conditions provided.
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
|
|
Top Courses for Class 10View all
If alpha ^ 2 * beta and alpha * beta ^ 2 are zeroes of the polynomial x ^ 2 + px + q where a, beta are zeroes of polynomial 3x ^ 2 - x + 6 then find the values of p and q.?
Question Description
If alpha ^ 2 * beta and alpha * beta ^ 2 are zeroes of the polynomial x ^ 2 + px + q where a, beta are zeroes of polynomial 3x ^ 2 - x + 6 then find the values of p and q.? 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 alpha ^ 2 * beta and alpha * beta ^ 2 are zeroes of the polynomial x ^ 2 + px + q where a, beta are zeroes of polynomial 3x ^ 2 - x + 6 then find the values of p and q.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha ^ 2 * beta and alpha * beta ^ 2 are zeroes of the polynomial x ^ 2 + px + q where a, beta are zeroes of polynomial 3x ^ 2 - x + 6 then find the values of p and q.?.
If alpha ^ 2 * beta and alpha * beta ^ 2 are zeroes of the polynomial x ^ 2 + px + q where a, beta are zeroes of polynomial 3x ^ 2 - x + 6 then find the values of p and q.? 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 alpha ^ 2 * beta and alpha * beta ^ 2 are zeroes of the polynomial x ^ 2 + px + q where a, beta are zeroes of polynomial 3x ^ 2 - x + 6 then find the values of p and q.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha ^ 2 * beta and alpha * beta ^ 2 are zeroes of the polynomial x ^ 2 + px + q where a, beta are zeroes of polynomial 3x ^ 2 - x + 6 then find the values of p and q.?.
Solutions for If alpha ^ 2 * beta and alpha * beta ^ 2 are zeroes of the polynomial x ^ 2 + px + q where a, beta are zeroes of polynomial 3x ^ 2 - x + 6 then find the values of p and q.? 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 alpha ^ 2 * beta and alpha * beta ^ 2 are zeroes of the polynomial x ^ 2 + px + q where a, beta are zeroes of polynomial 3x ^ 2 - x + 6 then find the values of p and q.? defined & explained in the simplest way possible. Besides giving the explanation of
If alpha ^ 2 * beta and alpha * beta ^ 2 are zeroes of the polynomial x ^ 2 + px + q where a, beta are zeroes of polynomial 3x ^ 2 - x + 6 then find the values of p and q.?, a detailed solution for If alpha ^ 2 * beta and alpha * beta ^ 2 are zeroes of the polynomial x ^ 2 + px + q where a, beta are zeroes of polynomial 3x ^ 2 - x + 6 then find the values of p and q.? has been provided alongside types of If alpha ^ 2 * beta and alpha * beta ^ 2 are zeroes of the polynomial x ^ 2 + px + q where a, beta are zeroes of polynomial 3x ^ 2 - x + 6 then find the values of p and q.? theory, EduRev gives you an
ample number of questions to practice If alpha ^ 2 * beta and alpha * beta ^ 2 are zeroes of the polynomial x ^ 2 + px + q where a, beta are zeroes of polynomial 3x ^ 2 - x + 6 then find the values of p and q.? 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