Consider the quadratic equation 2t2+(k−3)t+(k+5)=0, where k is a real parameter.
a. (i) Write the expression for the discriminant of the equation.
b. (ii) Determine the set of values of k for which the equation has two distinct real roots.
c. (iii) Find the value(s) of k for which the equation has equal real roots.
d. (iv) For what values of k does the equation have no real roots? Justify your answer.