Consider the quadratic equation ax2+bx+c=0 where a,b,c are real numbers and a=0. Answer the following:
a. (i) Write the expression for the discriminant D of the equation and describe how the sign of D determines the nature of the roots.
b. (ii) For the equation 5x2−4x+1=0, calculate the discriminant and comment on the nature of its roots.
c. (iii) Find the smallest real value of m such that the equation 5x2−4x+m=0 possesses two real and equal roots.