The resistance R_t of a conductor varies with temperature t as shown in the figure. If the variation is represented by ${\mathrm{R}}_{\mathrm{t}}={\mathrm{R}}_0\left[1+\mathrm{\alpha t}+{\mathrm{\beta t}}^2\right]$ , then

Since the value of R continuously increases, both $\mathrm{\alpha }$ and $\mathrm{\beta }$ must be positive.
Actually the components of the given equation are as follows

It $\mathrm{\alpha }$ is positive, $\mathrm{\beta }$ is negative, the component will be shown in the following graph.