Mathematics

Problem

Consider the quadratic equation

2x^2 + (k-5)x + k = 0

, where

k

is a real parameter. a. (i) Derive the expression for the discriminant

D

in terms of

k

. b. (ii) Find the set of all real values of

k

for which the equation has two distinct real roots. c. (iii) Determine the value(s) of

k

for which the equation has equal real roots. d. (iv) Find the set of all real values of

k

for which the equation has no real roots.