Mathematics

Problem

The quadratic equation

(k-5)x^{2}+2(k+1)x-8=0

depends on the real parameter

k

. a. (i) Find all real values of

k

that make the equation possess two distinct real roots. b. (ii) Among the values obtained in part (i), identify those for which the coefficient of

x^{2}

is positive. c. (iii) Hence, list every integer value of

k

that simultaneously satisfies the requirements of parts (i) and (ii).