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Question Number 91473 by A8;15: last updated on 01/May/20

Answered by MJS last updated on 01/May/20

$$x^4-22x^2+x+112=0$$$$\mathrm{first},\mathrm{testing}\mathrm{all}\mathrm{factors}\mathrm{of}\pm 112=\pm 2^{4}7$$$$\Rightarrow \mathrm{no}\mathrm{solution}$$$$\mathrm{second},\mathrm{trying}\mathrm{to}\mathrm{find}\mathrm{the}\mathrm{square}\mathrm{factors}$$$$(x^2-\alpha x-\beta )(x^2+\alpha x-\gamma )=x^4-22x^2+x+112$$$$\mathrm{by}\mathrm{matching}\mathrm{the}\mathrm{constants}$$$$\Rightarrow \mathrm{no}‘‘{\mathrm{nice}}^{″}\mathrm{solution}\mathrm{in}\mathrm{this}\mathrm{case}$$$$\mathrm{now}\mathrm{you}\mathrm{can}\mathrm{try}{\mathrm{Ferrari}}^{\prime }\mathrm{s}\mathrm{solution}\mathrm{but}\mathrm{it}\mathrm{will}$$$$\mathrm{not}\mathrm{be}\mathrm{useable}$$$$\Rightarrow \mathrm{approximate}$$$$x_1\approx -3.81841$$$$x_2\approx -2.75171$$$$x_3\approx 2.92139$$$$x_4\approx 3.64874$$

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