PrecalculusSuperchallengeSystems, Matrices, and Determinants

Systems, Matrices, and Determinants · Superchallenge problem

Consider the system

\begin{aligned}x+y+z&=1\\x+2y+4z&=b\\x+4y+10z&=b^2\end{aligned}

Find the sum of all real values of $b$ for which the system has at least one solution.