The line y = 3x-4 intersects the curve y = x^2 - a, where a is an unknown constant number. Find all possible values of a.

For the line and the curve to intersect we need the for the following system of equations to have a solution. y = 3x AND y = x² - aThe solution of the system of equations is found by solving x^2 - 3x - a = 0. (Interested in real numbers only)The solutions of a quadratic equation of the form ax^2 + bx + c = 0 can be obtained via the formula (-b +- sqrt(b^2 - 4ac) ) / (2a).The formula results in a valid (/real) value only when b^2 - 4ac >=0, which in our case is equivalent to 9 + 4a >= 0.As we are given that the two curve intersect, we must have 9 + 4a >= 0, and thus a can be any value greater or equal to -9/4.