kylamchavez
kylamchavez kylamchavez
  • 03-03-2018
  • Mathematics
contestada

Find the roots of the equation x^3-3x^2+x+5

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zhaotianyu369 zhaotianyu369
  • 03-03-2018
First observe that x=-1 is a root of the equation. Use long division to divide x^3-3x^2+x+5 by x+1, we find that (x^3-3x^2+x+5)/(x+1)=(x^2-4x+5). Now we need to find the roots of x^2-4x+5.
x^2-4x+5=0, 
x^2-4x+4=-1,
(x-2)^2=i,
x-2=i or -1,
x=2+i or 2-i. 
The three roots are 2+i, 2-i, -1.
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