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If alpha and beta are the zeros of polynomial f(x) = 3x^2 -5x -5. Evaluate alpha^2 + beta^2?
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If alpha and beta are the zeros of polynomial f(x) = 3x^2 -5x -5. Eval...
Explanation:
Given:
f(x) = 3x^2 - 5x - 5
Let alpha and beta be the zeros of the polynomial f(x).
Sum of Zeros:
By Vieta's formulas, the sum of the zeros of the polynomial is given by:
alpha + beta = -(-5)/3 = 5/3
Product of Zeros:
Similarly, the product of the zeros of the polynomial is given by:
alpha * beta = -5/3
Finding alpha^2 + beta^2:
We know that (alpha + beta)^2 = alpha^2 + beta^2 + 2alpha*beta
Expanding this expression, we get:
(alpha + beta)^2 = alpha^2 + beta^2 + 2*(-5/3)
(5/3)^2 = alpha^2 + beta^2 - 10/3
25/9 = alpha^2 + beta^2 - 10/3
alpha^2 + beta^2 = 25/9 + 10/3
alpha^2 + beta^2 = (25 + 30)/9
alpha^2 + beta^2 = 55/9
Therefore, alpha^2 + beta^2 = 55/9.
Given:
f(x) = 3x^2 - 5x - 5
Let alpha and beta be the zeros of the polynomial f(x).
Sum of Zeros:
By Vieta's formulas, the sum of the zeros of the polynomial is given by:
alpha + beta = -(-5)/3 = 5/3
Product of Zeros:
Similarly, the product of the zeros of the polynomial is given by:
alpha * beta = -5/3
Finding alpha^2 + beta^2:
We know that (alpha + beta)^2 = alpha^2 + beta^2 + 2alpha*beta
Expanding this expression, we get:
(alpha + beta)^2 = alpha^2 + beta^2 + 2*(-5/3)
(5/3)^2 = alpha^2 + beta^2 - 10/3
25/9 = alpha^2 + beta^2 - 10/3
alpha^2 + beta^2 = 25/9 + 10/3
alpha^2 + beta^2 = (25 + 30)/9
alpha^2 + beta^2 = 55/9
Therefore, alpha^2 + beta^2 = 55/9.
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If alpha and beta are the zeros of polynomial f(x) = 3x^2 -5x -5. Evaluate alpha^2 + beta^2?
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If alpha and beta are the zeros of polynomial f(x) = 3x^2 -5x -5. Evaluate alpha^2 + beta^2? 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 and beta are the zeros of polynomial f(x) = 3x^2 -5x -5. Evaluate alpha^2 + beta^2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are the zeros of polynomial f(x) = 3x^2 -5x -5. Evaluate alpha^2 + beta^2?.
If alpha and beta are the zeros of polynomial f(x) = 3x^2 -5x -5. Evaluate alpha^2 + beta^2? 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 and beta are the zeros of polynomial f(x) = 3x^2 -5x -5. Evaluate alpha^2 + beta^2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are the zeros of polynomial f(x) = 3x^2 -5x -5. Evaluate alpha^2 + beta^2?.
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