quadratic

[robust moss]

Please explain why only one root in 0,1 can't understand it

[paper kestrel]

Yeah, it's not obvious, took me a while to get it. Picture what the sin function does when it moves in the range [0, pi]. It starts at 0, grows up to 1 at pi/2, and then comes back down to zero it the same way it went up. So, it crosses each value between 0 and 1 twice. If you had two roots in (0,1), then it would cross both on the way up, and both on the way down, for a total of 4 roots. In order to have two distict roots, you need to have only one between zero and one: it'll cross it once on the way up, and onceon the way down

I suggest plotting it with different values of k to see it

[robust moss]

Thanks a lot