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Let alpha and beta be the roots of the e...

Let `alpha and beta` be the roots of the equation `x^(2)+ax+1=0, a ne0`. Then the equation whose roots are `-(alpha+(1)/(beta))` and `-((1)/(alpha)+beta)` is

A

`x^(2)=0`

B

`x^(2)-2ax+4=0`

C

`x^(2)-2ax+4=0`

D

`x^(2)-ax+1=0`

Text Solution

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The correct Answer is:
To solve the problem, we need to find the equation whose roots are given by the expressions involving the roots \( \alpha \) and \( \beta \) of the equation \( x^2 + ax + 1 = 0 \). ### Step 1: Identify the roots and their properties The roots of the equation \( x^2 + ax + 1 = 0 \) are \( \alpha \) and \( \beta \). By Vieta's formulas: - The sum of the roots \( \alpha + \beta = -a \) - The product of the roots \( \alpha \beta = 1 \)
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