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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.?
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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.
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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 2025 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 2025 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 2025 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 2025 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.?.
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