The resistance Rt of a conductor varies with temperature t as shown in the figure. If the variation is represented by Rt=R01+αt+βt2, then 

(1) α and β are both negative

(2) α and β are both positive

(3) α is positive and β is negative

(4) α is negative and β are positive

(3) Since the value of R continuously increases, both α and β must be positive.

Actually the components of the given equation are as follows

It α is positive, β is negative, the component will be shown in the following graph.

In this case, the value of R will not increase continuously. Hence the correct option is (3).

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