Q:

The roots of $x^2-2x+3=0$ are $\alpha$ and $\beta$. Find the equation whose roots are: $\alpha+2$, $\beta+2$. Not sure of answer in book. 

The roots of $x^2-2x+3=0$ are $\alpha$ and $\beta$. Find the equation whose roots are: $\alpha+2$, $\beta+2$. Not sure of answer in book. 
My working:
$\alpha+\beta=2, \alpha\beta=3$
$(\alpha+2)+(\beta+2)=\alpha+\beta+4=6$
$(\alpha+2)(\beta+2)=\alpha\beta+2(\alpha+\beta)=7$
Therefore, equation whose roots are $\alpha+2, \beta+2$ is $x^2-6x+7=0$
Answer in book is $x^2-6x+11=0$

A:

Note that
$$(\alpha+2)(\beta +2)=\alpha\beta+2(\alpha+\beta)\color{red}{+4}$$

