(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In the equation [tex]x^3+ax^2+bx+c=0[/tex]

the coefficients a,b and c are all real. It is given that all the roots are real and greater than 1.

(i) Prove that [tex]a<-3[/tex]

(ii)By considering the sum of the squares of the roots,prove that [tex]a^2>2b+3[/tex]

(iii)By considering the sum of the cubes of the roots,prove that [tex]a^3<-9b-3c-3[/tex]

2. Relevant equations

If the roots are A,B and C then A+B+C = a/1=a

ABC= -c/a

AB+AC+BC= b/a

3. The attempt at a solution

I do not know if there are any other formula for the squares/cubes of roots other than the ones i stated above; If there are any simpler ones please tell me.

I got out parts (ii) by taking (A+B+C)=a and appropriately squaring it, but I was unable to get out parts (i) and (iii), could someone please help me prove it..thanks

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# Homework Help: Roots of a cubic polynomial

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