Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 123025 by ajfour last updated on 21/Nov/20

Commented by ajfour last updated on 22/Nov/20

$$If\alpha ,\beta ,\gamma arerootsofcubiceq.$$$$x^3-x-c=0(0<c<\frac{2}{3\sqrt{3}});wirhthe$$$$helpofsuitablep,find\alpha .$$

Commented by ajfour last updated on 22/Nov/20

$$valueofpistobechosen,so$$$$thatthedegreefourcanbesolved$$$$ifnotthedegreethree.$$

Commented by mr W last updated on 22/Nov/20

$$whatshouldbep?$$

Commented by MJS_new last updated on 22/Nov/20

$$\mathrm{just}\mathrm{a}\mathrm{few}\mathrm{thoughts}...$$$$\mathrm{if}\alpha >0\wedge \beta <0\wedge \gamma <0\wedge \beta \ne \gamma \Rightarrow \alpha =-(\beta +\gamma )$$$$x^3+px+q=0\mathrm{with}p=-1\Rightarrow \beta =-\frac{\gamma }{2}\pm \frac{\sqrt{4-3{\gamma }^2}}{2}$$$$\Rightarrow c=\gamma ({\gamma }^2-1)$$$$\mathrm{introducing}p\mathrm{we}\mathrm{get}$$$$(x-p)(x-\gamma )(x-\frac{\gamma }{2}-\frac{\sqrt{4-3{\gamma }^2}}{2})(-\frac{\gamma }{2}+\frac{\sqrt{4-3{\gamma }^2}}{2})=0$$$$\mathrm{and}\mathrm{it}\mathrm{would}\mathrm{be}\mathrm{nice}\mathrm{if}p=-\gamma$$$$\mathrm{so}\mathrm{we}\mathrm{have}\mathrm{to}\mathrm{solve}c=\gamma ({\gamma }^2-1)\mathrm{for}\gamma \mathrm{but}\mathrm{this}$$$$\mathrm{is}\mathrm{exactly}\mathrm{the}\mathrm{same}\mathrm{problem}\mathrm{as}\mathrm{before}:$$$${\gamma }^3-\gamma -c=0$$$$\mathrm{I}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{think}\mathrm{we}\mathrm{can}\mathrm{find}\mathrm{any}\mathrm{fitting}p\mathrm{without}$$$$\mathrm{solving}\mathrm{this}{3}^{\mathrm{rd}}\mathrm{degree}\mathrm{polynome}...$$

Answered by ajfour last updated on 26/Nov/20

Terms of Service

Privacy Policy

Contact: info@tinkutara.com