Please help me with calculus

Question 2. (How many points of intersection?) Two different curves are parametrizationwing equations: (t) = 12, y (t ) = t+ +2 is the parametrization of the first curve, where t E R, and x(t) = 12, y(t) = 13 - 3t is the parametrization of the second curve, again with te R. (a) In an effort to determine where these two curves intersect, suppose we set the x-coordinates to be equal, and the y-coordinates to be equal, and endeavor to solve for the corresponding value(s) of t that produce intersection. The r-equation would just be t2 = t2, which is always satisfied. The y-equation is t + t2 = t3 - 3t, which (after some rearranging and factoring) becomes t ( t 2 - t - 4) = 0. Let's solve this equation using the quadratic formula. This gives the solutions: t =0, t= f+ v17 1 - V17 t = 2 2 We conclude that these two curves must intersect at three points or less. Is this correct? If not, where exactly is the flaw in our reasoning? (b) At how many distinct points do these two curves intersect? Find the exact coordinates (i.e. cartesian coordi- nates in the xy-plane) of all intersection points