Consider the quadratic equation 2x2+kx−3=0, where k is a real parameter.
a. (i) Find the set of all real values of k for which the equation has no real roots.
b. (ii) For k=8, determine the roots of the equation and hence obtain the x–intercepts of the graph of y=2x2+8x−3.
c. (iii) Sketch the graph of y=2x2+8x−3, clearly marking the vertex and the points where the graph meets the coordinate axes.