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If &, ẞ are the roots of the equation x ^ 2 - 5x + 6 = 0 then the equation with roots (alpha ^ 2 + beta) and (alpha + beta ^ 2) is?
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If &, ẞ are the roots of the equation x ^ 2 - 5x + 6 = 0 then the equa...


Given Information:

- Roots of the equation x^2 - 5x + 6 = 0 are & and ẞ.
Calculations:

Finding the sum and product of roots:

- Sum of roots, & + ẞ = 5
- Product of roots, & * ẞ = 6
Finding the new roots:

- Let the new roots be (α^2 + β) and (α + β^2)
- Sum of new roots = (α^2 + β) + (α + β^2) = α^2 + 2αβ + β^2 = (α + β)^2
- Product of new roots = (α^2 + β)(α + β^2) = α^3 + α^2β + αβ^2 + β^3 = α^3 + β^3 + 3αβ(α + β) = (α + β)^3
Final Equation:

- The equation with roots (α^2 + β) and (α + β^2) is x^2 - 5x + 6 = 0

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If &, ẞ are the roots of the equation x ^ 2 - 5x + 6 = 0 then the equation with roots (alpha ^ 2 + beta) and (alpha + beta ^ 2) is?
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If &, ẞ are the roots of the equation x ^ 2 - 5x + 6 = 0 then the equation with roots (alpha ^ 2 + beta) and (alpha + beta ^ 2) is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If &, ẞ are the roots of the equation x ^ 2 - 5x + 6 = 0 then the equation with roots (alpha ^ 2 + beta) and (alpha + beta ^ 2) is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If &, ẞ are the roots of the equation x ^ 2 - 5x + 6 = 0 then the equation with roots (alpha ^ 2 + beta) and (alpha + beta ^ 2) is?.
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