The sum of all possible values of $k$ for which the polynomials $x^2-3 x+2$ and $x^2-5 x+k$ have a r

Question

The sum of all possible values of $k$ for which the polynomials $x^2-3 x+2$ and $x^2-5 x+k$ have a root in common is

Professor PC Thomas Classes · Answer

Roots of first are 1, 2. If 1 is root of second: $1-5+k=0 \Rightarrow k=4$. If 2 is root: $4-10+k=0 \Rightarrow k=6$. Sum $4+6=10$.