Question

Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.

f(x) = -2x4 + 4x3 + 3x2 + 18

Answer 1

do you have an idea how to use rational zero theorem?

Answer 2

let p/q be a rational number such that f(p/q) = 0

possible p values: plus or minus (1,2,3,6,9,18)
possible q values : plus or minus (1,2)

Answer 3

f(x) = -2x^4 + 4x^3 + 3x^2 + 18

Answer 4

@jim_thompson5910

Answer 5

List all the factors of 18: 1,2,3,6,9,18

Then list all the factors of -2: 1, 2

Now divide each number from the first list by each number in the second list


1/1,2/1,3/1,6/1,9/1,18/1, 1/2,2/2,3/2,6/2,9/2,18/2

which simplifies to


1,2,3,6,9,18, 1/2,1,3/2,3,9/2,6


and that further simplifies to


1/2, 1, 3/2, 2, 3, 9/2, 6, 9, 18


Then negate everything to double the list to get


1/2, 1, 3/2, 2, 3, 9/2, 6, 9, 18
-1/2, -1, -3/2, -2, -3, -9/2, -6, -9, -18

Answer 6

So the list of all possible rational roots are:

1/2, 1, 3/2, 2, 3, 9/2, 6, 9, 18
-1/2, -1, -3/2, -2, -3, -9/2, -6, -9, -18

Answer 7

thank you so muchhhh :D

Answer 8

np