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If x, ẞ are the roots of the equation x ^ 2 - 5x + 6 = 0 then the equation with roots (alpha + beta) and (alpha - beta) is:?
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If x, 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 x and ß.
Finding the roots:
The given equation can be factored as (x - 2)(x - 3) = 0. So, the roots are x = 2 and x = 3.
Sum and product of roots:
- Sum of the roots (α + β) = 2 + 3 = 5
- Product of the roots (αβ) = 2 * 3 = 6
Equation with roots (α + β) and (α - β):
Let the roots of the new equation be (α + β) and (α - β). The new equation can be written as:
(x - (α + β))(x - (α - β)) = 0
Expanding this equation, we get:
x^2 - [(α + β) + (α - β)]x + (α + β)(α - β) = 0
x^2 - 2αx + (α^2 - β^2) = 0
x^2 - 2αx + (α^2 - β^2) = 0
Since α + β = 5 and αβ = 6, we can find α and β:
α = (α + β)/2 = 5/2 = 2.5
β = (α - β)/2 = 1/2 = 0.5
Substitute the values of α and β in the equation:
x^2 - 2(2.5)x + (2.5^2 - 0.5^2) = 0
x^2 - 5x + 6 = 0
Therefore, the equation with roots (α + β) and (α - β) is x^2 - 5x + 6 = 0.
- Roots of the equation x^2 - 5x + 6 = 0 are x and ß.
Finding the roots:
The given equation can be factored as (x - 2)(x - 3) = 0. So, the roots are x = 2 and x = 3.
Sum and product of roots:
- Sum of the roots (α + β) = 2 + 3 = 5
- Product of the roots (αβ) = 2 * 3 = 6
Equation with roots (α + β) and (α - β):
Let the roots of the new equation be (α + β) and (α - β). The new equation can be written as:
(x - (α + β))(x - (α - β)) = 0
Expanding this equation, we get:
x^2 - [(α + β) + (α - β)]x + (α + β)(α - β) = 0
x^2 - 2αx + (α^2 - β^2) = 0
x^2 - 2αx + (α^2 - β^2) = 0
Since α + β = 5 and αβ = 6, we can find α and β:
α = (α + β)/2 = 5/2 = 2.5
β = (α - β)/2 = 1/2 = 0.5
Substitute the values of α and β in the equation:
x^2 - 2(2.5)x + (2.5^2 - 0.5^2) = 0
x^2 - 5x + 6 = 0
Therefore, the equation with roots (α + β) and (α - β) is x^2 - 5x + 6 = 0.
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If x, ẞ are the roots of the equation x ^ 2 - 5x + 6 = 0 then the equation with roots (alpha + beta) and (alpha - beta) is:?
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If x, ẞ are the roots of the equation x ^ 2 - 5x + 6 = 0 then the equation with roots (alpha + beta) and (alpha - beta) 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 x, ẞ are the roots of the equation x ^ 2 - 5x + 6 = 0 then the equation with roots (alpha + beta) and (alpha - beta) is:? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x, ẞ are the roots of the equation x ^ 2 - 5x + 6 = 0 then the equation with roots (alpha + beta) and (alpha - beta) is:?.
If x, ẞ are the roots of the equation x ^ 2 - 5x + 6 = 0 then the equation with roots (alpha + beta) and (alpha - beta) 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 x, ẞ are the roots of the equation x ^ 2 - 5x + 6 = 0 then the equation with roots (alpha + beta) and (alpha - beta) is:? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x, ẞ are the roots of the equation x ^ 2 - 5x + 6 = 0 then the equation with roots (alpha + beta) and (alpha - beta) is:?.
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