2 A line has equation \(y = 2 c x + 3\) and a curve has equation \(y = c x ^ { 2 } + 3 x - c\), where \(c\) is a constant.
Showing all necessary working, determine which of the following statements is correct.
A The line and curve intersect only for a particular set of values of \(c\).
B The line and curve intersect for all values of \(c\).
C The line and curve do not intersect for any values of \(c\).