Question

If alpha and beta are the zeros of polynomial p(x)=3x^2+2x+1,find the polynomial whose zeroes are alpha-1/alpha+1 and beta-1/beta+1​

Answer 1

Answer:

$\frac{(1 - \alpha )(1 - \beta ) }{(1 + \alpha )(1 + \beta )}$

$\frac{(1 - \alpha - \beta + \alpha \beta ) }{(1 + \alpha + \beta = \alpha \beta )}$

$( \frac{1 - ( \alpha + \beta ) + \alpha \beta }{1 + ( \alpha + \beta ) + \alpha \beta } )$

$|1 + \frac{2}{3} + \frac{1}{3} | | \div 1 - \frac{2}{3} + \frac{1}{3} |$

$( \frac{2 \times 3}{2} ) = 3$

$= \frac{(1 - \alpha )(1 + \beta ) + (1 - \beta )(1 + \alpha )}{(1 + \alpha + \beta + \alpha \beta )}$

$= \frac{1 + \beta - \alpha - \alpha \beta + 1 + \alpha - \beta - \alpha \beta }{ \frac{2}{3} }$

$= \frac{3(2 - 2 \alpha \beta )}{2}$

$= 3(1 - \alpha \beta )$

$= 3(1 - \frac{1}{3} )$

$= 2 \: \: (ans)$

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