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