If the number of times the equation touches the x-axis is its number of roots, then the degree of the polynomial, which is 2n, should be the answer. Now, there is no restriction on what n could be. If n=1, the number of roots is 2 x 1=2. If n=4, it would be 2 x 4=8. Hence shouldn’t D be the correct answer?
2n counts all complex solutions, but we only care for real solutions.
sorry can you expound on that further?
Take x^3 = -1, for example. This has only one real solution of x = -1 over \mathbb{R}. The remaining two are complex solutions. (I mean our real solutions are technically complex too but anyway that’s besides my point).
This only holds if we’re talking about the number of complex roots counting multiplicity.
An example to explain the “multiplicity” part could be as follows: x^2 = 0. There’s one real root here (x = 0) with multiplicity 2.