Question 4240: find all of the roots of these equations:
x^3-2x^2-2x-3
x^3+x^2+x+1
x^4+3x^3+3x^2+3x+2
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! i) x^3-2x^2-2x-3
= x^3 -3x^2 + x^2-2x-3
= x^2(x-3)-(x^2-2x-3)
= x^2(x-3)-(x-3)(x+1)
= (x-3)(x^2-x-1)
Roots are 3, [1+sqrt(5)]/2, [1-sqrt(5)]/2
ii) x^3+x^2+x+1
= x^2(x+1) +(x+1)
= (x+1)(x^2+1)
Roots are -1,i and -i.
(iii) x^4+3x^3+3x^2+3x+2
= (x^4+ x^3)+ (2x^3+ 2x^2)+ (x^2+3x+2 )
= x^3(x+1) + 2x^2(x+1) + (x+1)(x+2)
= (x+1)[x^3+2x^2+x+2]
= (x+1)(x+2)(x^2+1)
Roots are -1,-2,i, & -i
Kenny
|
|
|
