Answer the following questions related to the quadratic expression ax2+bx+c(a=0).
(i) State the relationship between the value of b2−4ac and the nature of the roots of the quadratic equation ax2+bx+c=0.
(ii) Calculate b2−4ac for each of the following equations:
(a) 3x2+4x−2=0
(b) 2x2+5x+3=0
(c) 4x2+4x+1=0.
(iii) Classify each equation in part (ii) as having two distinct real roots, one repeated real root, or no real roots, giving a brief reason in each case.
(iv) Among the equations in part (ii), identify the one whose graph would touch the x-axis at exactly one point. Justify your answer.