The first equation is a quartic, and it has 4 roots. Newton's method only returns 1 root though, and you are asked to find 2. But you are given the interval of two of the roots, so if you pick a starting value in each of those intervals, it is likely to converge to the root in that interval, and not another root. So do the process twice for that questions, the first time use a starting value from the first interval, and the 2nd time use a starting value from the 2nd interval and you should get two different answers which are both correct.

For the exponential:

Just use a calculator when inputting the numbers...