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If alpha and beta are the zeros of the q...

If `alpha and beta` are the zeros of the quadratic polynomial `f (x)= x^2-2x+3`, find a polynomial whose roots are (i) `alpha-2,beta-2` (ii) `(alpha-1)/(alpha+1),(beta-1)/(beta+1)`

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1)`x^2-2x+3`
`alpha+beta=2`
`alpha*beta=3`
`x^2-((alpha-2)(+(beta-2))x+(alpha-2)(beta-2)`
`alpha-2+beta-2=(alpha+beta-4)`
`(alpha-2)(beta-2)=alphabeta-2beta-2alpha+4`
`3-2(2)+4=3`
`x^2+2x+3=0`.
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