Let k be a real number. Examine the quadratic equation
(k+2)x2+4kx+3=0.
(i) Write down any value of k for which the expression fails to be a quadratic, and explain why this value must be excluded from further consideration.
(ii) For the admissible values of k, determine the set of all real numbers k for which the equation has no real roots.
(iii) From the set obtained in part (ii), identify the smallest positive integer value of k (if any) that satisfies the required condition.