Attempt all parts of the question given below.
(i) Two real numbers α and β satisfy α+β=3 and α−β=1. Determine the values of α and β.
(ii) Construct the monic quadratic polynomial that has α and β as its zeros.
(iii) Factorise the polynomial obtained in part (ii) and confirm that the factors yield the same zeros.
(iv) Using the polynomial from part (ii), calculate its value at x=2. Interpret this result with reference to the Factor Theorem.