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If alpha ands beta are the zeros of the polynomial 2x² -5x +7 , find a polynomial whose zeros are 2alpha +_ 3beta?
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If alpha ands beta are the zeros of the polynomial 2x² -5x +7 , find a...
Finding a Polynomial with Zeros 2alpha ± 3beta
Given Polynomial:
The given polynomial is 2x² - 5x + 7 with zeros alpha and beta.
Finding the Sum and Product of Zeros:
Let's find the sum and product of the zeros:
Sum of zeros = alpha + beta = 5/2
Product of zeros = alpha * beta = 7/2
Finding the New Zeros:
We need to find the zeros of the new polynomial which are 2alpha ± 3beta.
Zeros for 2alpha + 3beta:
2alpha + 3beta = 2(alpha + beta) + beta = 2(5/2) + beta = 5 + beta.
Zeros for 2alpha - 3beta:
2alpha - 3beta = 2(alpha + beta) - beta = 2(5/2) - beta = 5 - beta.
Forming the New Polynomial:
Now, we have the new zeros as 5 + beta and 5 - beta.
The new polynomial with these zeros can be formed as:
(x - (5 + beta))(x - (5 - beta)) = (x - 5 - beta)(x - 5 + beta) = x² - 5x + beta² - 25
Therefore, the polynomial with zeros 2alpha ± 3beta is x² - 5x + beta² - 25.
Given Polynomial:
The given polynomial is 2x² - 5x + 7 with zeros alpha and beta.
Finding the Sum and Product of Zeros:
Let's find the sum and product of the zeros:
Sum of zeros = alpha + beta = 5/2
Product of zeros = alpha * beta = 7/2
Finding the New Zeros:
We need to find the zeros of the new polynomial which are 2alpha ± 3beta.
Zeros for 2alpha + 3beta:
2alpha + 3beta = 2(alpha + beta) + beta = 2(5/2) + beta = 5 + beta.
Zeros for 2alpha - 3beta:
2alpha - 3beta = 2(alpha + beta) - beta = 2(5/2) - beta = 5 - beta.
Forming the New Polynomial:
Now, we have the new zeros as 5 + beta and 5 - beta.
The new polynomial with these zeros can be formed as:
(x - (5 + beta))(x - (5 - beta)) = (x - 5 - beta)(x - 5 + beta) = x² - 5x + beta² - 25
Therefore, the polynomial with zeros 2alpha ± 3beta is x² - 5x + beta² - 25.
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If alpha ands beta are the zeros of the polynomial 2x² -5x +7 , find a polynomial whose zeros are 2alpha +_ 3beta?
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If alpha ands beta are the zeros of the polynomial 2x² -5x +7 , find a polynomial whose zeros are 2alpha +_ 3beta? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If alpha ands beta are the zeros of the polynomial 2x² -5x +7 , find a polynomial whose zeros are 2alpha +_ 3beta? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha ands beta are the zeros of the polynomial 2x² -5x +7 , find a polynomial whose zeros are 2alpha +_ 3beta?.
If alpha ands beta are the zeros of the polynomial 2x² -5x +7 , find a polynomial whose zeros are 2alpha +_ 3beta? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If alpha ands beta are the zeros of the polynomial 2x² -5x +7 , find a polynomial whose zeros are 2alpha +_ 3beta? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha ands beta are the zeros of the polynomial 2x² -5x +7 , find a polynomial whose zeros are 2alpha +_ 3beta?.
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