polys (1 Viewer)

[Timothy.Siu]

if the roots of the equation x^3+3x^2-2x+1=0 are a,b,c, find the value of

a)a^2(b+c)+b^2(a+c)+c^2(a+b)

 

[Iruka]

a^2(b+c)+b^2(a+c)+c^2(a+b) = ab(a+b+c) + ac(a+b+c) + bc(a+b+c) - 3abc

 

[azureus88]

a^2(b+c)+b^2(a+c)+c^2(a+b) = ab(a+b+c) + ac(a+b+c) + bc(a+b+c) - 3abc

how are you supposed to see that coming, or it just somethin you're meant to remember?

 

[gurmies]

my god, that's a wild-ball of a question. I saw the word "polys", one of my favourite topics and thought, "time to solve some questions." The only way I can think of is to do what was suggested, to go sum of roots multiplied by sum of roots taken two at a time and account for any terms you have added on.

 

[Trebla]

It's not that hard. Just expand, collect terms and factorise. You should discover the pattern when you group them.