Mathematics

Problem

Consider the quadratic equation

x^{2}+2(k-1)x+k=0

, where

k

is a real parameter. a. (i) Express the discriminant of the equation in terms of

k

. b. (ii) Hence determine all integer values of

k

for which the equation has real and equal roots. c. (iii) For each value of

k

obtained in part (ii), find the common root of the equation.