Question 269865: I need help on finding the potential rational zeros of the polynomial function
f(x) = -4x^4 + 3x^2 - 4x + 6
Found 2 solutions by drk, Edwin McCravy:
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website! First we apply P - N - I to help us view sign changes and possible combinations.
P . . . . N . . . . I
3 . . . . 1 . . . .0
1 . . . . 1 . . . .2
So we know that there must be 1 real negative root.
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next we apply P / Q as
P: +-1, +-2, +-3, +-6
Q: +-1, +-2, +-4
we take all possible fractions and get:
P/Q = +-1, +-1/2 +-1/4, +-2, +-3, +-3/2, +-3/4, +-6
This is our list of potential rational zeros
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website! need help on finding the potential rational zeros of the polynomial function
f(x) = -4x4 + 3x2 - 4x + 6
All rational zeros of a polynomial in descending order,
if there are any, are fractions with a numerator which
is ± an integer factor of the last term in absolute value,
and a denominator which is ± an integer factor of the first
coefficient in absolute value.
The factors of the last term, 6, in absolute value are
1, 2, 3, 6
The factors of the first coefficient, -4, in absolute value
are
1,2,4.
No we make all possible fractions which have a numerator
of 1,2,3,or 6 and a denominator 1,2, or 4:
1/1, 1/2, 1/4, 2/1, 2/2. 2/4, 3/1, 3/2. 3/4, 6/1, 6/2, 6/4
Now we reduce them all
1, 1/2, 1/4, 2, 1. 1/2, 3, 3/2. 3/4, 6, 3, 3/2
Now we remove the duplications:
1, 1/2, 1/4, 2, 3, 3/2, 3/4, 6.
Now we put ± beside them all:
±1, ±1/2, ±1/4, ±2, ±3, ±3/2, ±3/4, ±6.
If there are any rational zeros, they are among
these 16.
Edwin
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