Expert: Abe Mantell - 1/5/2012

Question
1.) List the possible rational roots of the following equation:
   5x4 + 9x3 + 5x2 + 2x + 4 = 0

2.) List the possible rational roots of the following equation:
   3x4 + 5x3 + 3x2 - 7x + 9 = 0

3.) Find all the roots of the equation:
   x4 + 2x + 2 = 0

4.) Find all the roots of the equation:
   x4 + 3x3 - x2 - 9x - 6 = 0

5.) Find all the roots of the equation:
   2x3 - 5x2 - 11x - 4 = 0

Answer
Hello Maggie,

The rational root theorem tells us that the possible rational roots of a polynomial
with integer coefficients are factors of the constant term divided by factors of
the leading coefficient.
1) (factors of 4)/(factors of 5) ==> (1, -1, 2, -2, 4, -4)/(1, -1, 5, -5)
==> 1, -1, 1/5, -1/5, 2, -2, 2/5, -2/5, 4, -4, 4/5, -4/5

2) (factors of 3)/(factors of 9) ==> (1, -1, 3, -3)/(1, -1, 3, -3, 9, -9)
==> (1, -1, 1/3, -1/3, 1/9, -1/9, 3, -3)

3) (factors of 1)/(factors of 2) ==> 1, -1, 1/2, -1/2

4) (factors of 1)/(factors of -6) ==> 1, -1, 1/2, -1/2, 1/3, -1/3, 1/6, -1/6

5) (factors of 2)/(factors of -4) ==> 1, -1, 1/2, -1/2, 1/4, -1/4, 2, -2

I hope this helps.

Abe