Question 43192: List the potential rational zeros of the function below.
f(x) = 6x^4 + 2x^3 - 3x^2 + 2
a. 1/6, -1/6, 1/2, -1/2, 1/3, -1/3, 2/3, -2/3, 1, -1, 2, -2
b. 1/6, -1/6, 1/2, -1/2, 1/3, -1/3, 2/3, -2/3, 1, -1, 2, -2, 3, -3
c. 1/6, -1/6, 1/2, -1/2, 1/3, -1/3, 1, -1, 2, -2
d. 1/2, -1/2, 3/2, -3/2, 1, -1, 2, -2, 3, -3, 6, -6
e. None of the others
Found 2 solutions by Nate, stanbon:
Answer by Nate(3500)   (Show Source):
You can put this solution on YOUR website! f(x) = 6x^4 + 2x^3 - 3x^2 + 2
factors of  = 1,2
factors of  = 1,2,3,6
a/b and -a/b
1, 2, 1/2, 1/3, 2/3, 1/6, -1, -2, -1/2, -1/3, -2/3, -1/6
(A)
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! f(x) = 6x^4 + 2x^3 - 3x^2 + 2
a. 1/6, -1/6, 1/2, -1/2, 1/3, -1/3, 2/3, -2/3, 1, -1, 2, -2
b. 1/6, -1/6, 1/2, -1/2, 1/3, -1/3, 2/3, -2/3, 1, -1, 2, -2, 3, -3
c. 1/6, -1/6, 1/2, -1/2, 1/3, -1/3, 1, -1, 2, -2
d. 1/2, -1/2, 3/2, -3/2, 1, -1, 2, -2, 3, -3, 6, -6
e. None of the others
If p/q is a rational root of f(x) then p divides 2 and q divides 6
Therefore p can be 1,-1,2,-2
and q can be 1,-1,2,-2,3,-3,6,-6
"a" is the answer. Can you see why?
Cheers,
Stan H.
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