MT171 - FEEDBACK on QUESTION SHEET 3 - 2018/19 MARKING COMMENTS Questions marked are: Q1(a)/Q2(a) and (b)/ Q2(e) and (h)/ Q4 (guidelines and graph)/Q4(Mathematica) Each question will be classified as 0-if it is mostly incorrect; 1-if it is about half correct;2-if it is mostly correct. The maximum you can get is 10. For continuous assessment: if you didn't do enough work or gave in your work after the deadline, there will be a box encircling a zero at the top of page 1 of your work. Otherwise your work will have gained a 'one' and nothing will appear written. To gain a mark '1' you need to have completed the questions in Mathematica: print out your Mathematica notebook work and staple it to your conventional solutions. Comment 1 (C1) You need to improve the clarity of your presentation. Comment 2 (C2) Explain what you are doing. Give the arguments that are needed. Comment 3 (C3) Use correct notation! An equation needs to be written here. This needs a LHS (left hand side) and a RHS (right hand side)! Comment 4 (C4) Use correct mathematical language. Comment 5 (C5) No print out of your Mathematica notebook: mark '0' for Continuous Assessment (C.A.). Q1 (a) Comment 1.1 (C1.1) Descartes Rule of signs only tells you at most how many zeros has a polynomial. Intermediate Value Theorem tells you at least how many zeros has the polynomial. You need to combine the information from both to be able to conclude how many zeros there are, precisely (see solutions and lecture notes). Comment 1.2 (C1.2) You need to show the number of changes of sign in the coefficients of the polynomials. From there you conclude at most how many zeros has a polynomial but state that you are using Descartes Rule of Signs. Comment 1.3 (C1.3) When using Intermediate Value Theorem, evaluate p(x) for several values of x; then show that p(x1) p(x2)<0; you can then conclude that there is at least one zero in the interval (x1,x2): not that you have a zero in (X1,X2)! Comment 1.4 (C1.4) You need to write once Descartes Rule of Signs (DRS) to be able to use DRS after. The same with Intermediate Value Theorem (IVT) to use IVT after. Comment 1.5 (C1.5) You need to state that you are using the Intermediate Value Theorem. Comment 1.6 (C1.6) You need to combine the Descartes Rule of Signs with the Intermediate Value Theorem to conclude how many zeros there are precisely.
Comment 1.7 (C1.7) Your work is a confusion. You need to be systematic: use first DRS and then IVT. Then combine the results from both to conclude about the precise location of zeros of the polynomial. Comment 1.9 (C1.9) Zeros of a function! Roots are solutions of the equation f(x)=0. Comment 1.10 (C1.10) Descartes Rule of Signs considers a polynomial, not an equation. You need to study p(x) and p(-x) and not the equation you get from writing those equal to zero! Comment 1.11 (C1.11) You are