Question Number 184872 by CrispyXYZ last updated on 13/Jan/23
![An odd function f(x) whose domain is R satisfies f(x)=f(x+2). When x ∈ (0, 1), f(x)=−2x^2 +ax−2. If f has 2023 zeros in [0, 1011]. Then the range of a can be ? A. [−6, −2(√2)] B. [−4, −2(√2)] C. [−8, −6] D. [−6, −4]](https://www.tinkutara.com/question/Q184872.png)
$$\mathrm{An}\:\mathrm{odd}\:\mathrm{function}\:{f}\left({x}\right)\:\mathrm{whose}\:\mathrm{domain}\:\mathrm{is}\:\mathbb{R} \\ $$$$\mathrm{satisfies}\:{f}\left({x}\right)={f}\left({x}+\mathrm{2}\right).\:\mathrm{When}\:{x}\:\in\:\left(\mathrm{0},\:\mathrm{1}\right), \\ $$$${f}\left({x}\right)=−\mathrm{2}{x}^{\mathrm{2}} +{ax}−\mathrm{2}. \\ $$$$\mathrm{If}\:{f}\:\mathrm{has}\:\mathrm{2023}\:\mathrm{zeros}\:\mathrm{in}\:\left[\mathrm{0},\:\mathrm{1011}\right].\:\mathrm{Then}\:\mathrm{the} \\ $$$$\mathrm{range}\:\mathrm{of}\:{a}\:\mathrm{can}\:\mathrm{be}\:? \\ $$$$\mathrm{A}.\:\left[−\mathrm{6},\:−\mathrm{2}\sqrt{\mathrm{2}}\right]\:\:\:\:\:\:\:\:\mathrm{B}.\:\left[−\mathrm{4},\:−\mathrm{2}\sqrt{\mathrm{2}}\right] \\ $$$$\mathrm{C}.\:\left[−\mathrm{8},\:−\mathrm{6}\right]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{D}.\:\left[−\mathrm{6},\:−\mathrm{4}\right] \\ $$