SOLUTION: Use the Rational Root Theorem to list all possible rational roots for each equation. Then find any actual roots. x^3+2x^2+3x+6=0

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Use the Rational Root Theorem to list all possible rational roots for each equation. Then find any actual roots. x^3+2x^2+3x+6=0      Log On


   

Question 458709: Use the Rational Root Theorem to list all possible rational roots for each equation. Then find any actual roots.
x^3+2x^2+3x+6=0
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Applying the rational root theorem, possible rational roots are -6, -3,-2, -1, 1,2,3,6.
Using the remainder theorem (or synthetic division), trying out x = -2:
%28-2%29%5E3+%2B+2%28-2%29%5E2+%2B+3%28-2%29+%2B+6+=+0 Hence x = -2 is a rational root. After synthetic division, the quotient is x%5E2+%2B+3, which doesn't even have real roots.