That was a nice question and great explanation. The last part working out value of k seemed a bit pointless and tedious. I thought I had seen something similar before, just checked and it virtually the same as an example given in Pure Mathematics 2 by Bostock and Chandler, the old 1979 version. It basically uses it to prove that if a polynomial f(x) has repeated factors (x-a)^n, then f'(x) will have repeated factors (x-a)^(n-1). Any future STEP students should consider getting that book, can buy it second hand for about £5. Even if it is just for the three chapters on functions and their properties, some curves and their properties and polynomial functions and equations. Or splash out and get both parts 1 and 2 of the older versions, there are lots of STEP style questions in them. They also have applied books 1 and 2, I have seen so many STEP mechanics questions that are basically the same as questions or examples in those books. They are obviously written in an older more formal style than the books of today.
