i need more help with this problem:

the question is to identify all the real roots of 4x^4+31x^3-4x^2-89x+22=0

Question

i need more help with this problem:

the question is to identify all the real roots of 4x^4+31x^3-4x^2-89x+22=0

dumbcow · Answer

i would use synthetic division to try to find one root
possible roots are +-1, +-2, +-11, +-22

anonymous · Answer

the answer is -2, 1/4, -3, $$2\sqrt{5}$$, -3 and $$-2\sqrt{5}$$

anonymous · Answer

i just dont know how to get to the answers

dumbcow · Answer

well using synthetic division, you find -2 is a root
so after factoring out (x+2), you have

-> (x+2)(4x^3+23x^2-50x+11)
From there you have to find another root so you can factor it out
try +-1, +-11, +-22, +-1/2, +-1/4

dumbcow · Answer

this comes from the rational root theorem
a root must be a rational formed by factors of first and last coefficients

dumbcow · Answer

these can be a pain because there can be many possible combinations to try
you can also graph the function to get a general idea of what the roots may be