Part (a). This is a typical discriminant concept question. You should have learnt that for there to be two points of intersection between a curve and line, the discriminant of the equation of the curve and line equated together is > 0. Leave a comment if you still need help / clarifications!

Part (b). This part only involves 1 curve and the discriminant of 1 particular quadratic equation tells you how many roots it has. For the curve to be always positive, it must lie entirely above the x axis, meaning it has no real and distinct roots, so set the discriminant to <0, and solve the quadratic inequality to get your answer. Leave a comment if you still need help / clarifications