Question Number 200589 by Ikbal last updated on 20/Nov/23
Answered by Frix last updated on 20/Nov/23
$$\mathrm{First}\:\mathrm{try}\:\mathrm{factors}\:\mathrm{of}\:\pm\mathrm{40}\:\Rightarrow \\ $$$${x}^{\mathrm{4}} −\mathrm{3}{x}^{\mathrm{2}} −\mathrm{42}{x}−\mathrm{40}= \\ $$$$=\left({x}+\mathrm{1}\right)\left({x}−\mathrm{4}\right)\left({x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{10}\right) \\ $$$$\Rightarrow \\ $$$${x}=−\mathrm{1}\vee{x}=\mathrm{4}\vee{x}=−\frac{\mathrm{3}}{\mathrm{2}}\pm\frac{\sqrt{\mathrm{31}}}{\mathrm{2}}\mathrm{i} \\ $$