(b) $E = \alpha T + \frac{1}{2}\beta T^{2}$
For inversion temperature
$E = 0,\ \ T = \frac{- 2\alpha}{\beta}$
Thermo electric power
$P = \frac{dE}{dT} = \alpha + \frac{1}{2}\beta.(2T) \Rightarrow \alpha + \beta.T$
$\alpha + \beta\left( \frac{- 2\alpha}{\beta} \right) = \alpha - 2\alpha = - \alpha$