Examine the quadratic equation x2+2(k−1)x+(k+3)=0.
a. (i) State the discriminant of a quadratic equation ax2+bx+c=0 and briefly explain how its sign determines the nature of the roots.
b. (ii) Without solving the equation, determine the nature of the roots when (a) k=2 and (b) k=−5, giving reasons in each case.