From Förberedande kurs i matematik 1

If \displaystyle x=\text{1 } is a root of the equation, the equation should be satisfied if we substitute in \displaystyle x=\text{1 } into it,

i.e.

\displaystyle 1^{2}+4\centerdot 1+b=5+b should be equal to zero, and this gives directly that \displaystyle b=-\text{5}.