<s>[INST] Find the polynomial If $a$ and $b$ are the zeros of a polynomial $p(x) = x^2 - x-2$, find a polynomial whose zeroes are $2a+1$ and $2b+1$.
[Hint: I know that if we have the value of $\alpha + \beta$ and $\alpha\beta$, where $\alpha$ and $\beta$ are the roots of the required polynomial, then we can apply the formula $x^2 - (\alpha + \beta)x + (\alpha\beta)$.]
 [/INST] If x is a root of $x^2-x-2=0,$  we need to find an equation in $y$ such that $y=2x+1\implies x=\frac{y-1}2$
As x is a root of $x^2-x-2=0$,
$$ \left(\frac{y-1}2\right)^2-\frac{y-1}2-2=0\implies (y-1)^2-2(y-1)-8=0\implies y^2-4y-5=0$$
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