Question:
If $\alpha$ and $\beta$ are the zeros of the quadratic polynomial $f(x)=x^{2}-2 x+3$, find a polynomial whose roots are
$(i) \alpha+2, \beta+2$
(ii) $\frac{\alpha-1}{\alpha+1}, \frac{\beta-1}{\beta+1}$.
Solution:
(i) Since $\alpha$ and $\beta$ are the zeros of the quadratic polynomial $f(x)=x^{2}-2 x+3$
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