SOLUTION: Use the Rational Root Teorem to list all possible rational roots. Then find any actual roots. Please explain step by step. x^4-7x^2+12=0

Algebra ->  Radicals -> SOLUTION: Use the Rational Root Teorem to list all possible rational roots. Then find any actual roots. Please explain step by step. x^4-7x^2+12=0      Log On


   

Question 394496: Use the Rational Root Teorem to list all possible rational roots. Then find any actual roots.
Please explain step by step.
x^4-7x^2+12=0
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The possible rational roots are +/- 12, +/-6, +/-4, +/-3, +/-2, +/-1.
You can use synthetic division, or you can use the remainder theorem to try out the candidates:
2%5E4-7%2A2%5E2%2B12=0, and %28-2%29%5E4-7%28-2%29%5E2%2B12=0.
Incidentally 2, -2 are the only rational roots. The other roots (irrational ) come from the factor x%5E2+-+3 (obtained from synthetic division).