 In this video, we provide the solution to question number 10 for the practice final exam for math 1050 We're given a polynomial function. It's factored. We have 2x cube times x minus 1 squared times x plus 3 times 2x minus 1 to the fourth power At which x intercepts for this polynomial do we touch but not cross the x-axis? So we're looking for you know, if we want to touch but not cross we're looking for even multiplicities here And so that's going to happen at x minus one and at 2x minus One you have even multiplicities there. So the root associated to x minus one would be positive one The root associated to 2x minus one would be one half And so we see the correct answer the choice e x equals one and one half