If α and β are the zeros of the quadratic polynomial f(x)

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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