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

find all the factors of contant term, 18

Answer 2

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

Answer 3

factors of \(18 = \pm 1, \pm 2, \pm 3, \pm 6, \pm 9, \pm 18 \)

Answer 4

next, find all factors of leading coefficient
f(x) = -2x4 + 4x3 + 3x2 + 18
^

Answer 5

factors of \(2 = \pm ,1 \pm 2\)

Answer 6

possible rational zeroes are the ratios of both

Answer 7

so all the factors and their ratios? or just the ratios?

Answer 8

just the ratios

Answer 9

possible rational roots = \(\large \pm \frac{1}{1} , \pm \frac{2}{1} ,\pm \frac{3}{1} ,\pm \frac{6}{1} ,\pm \frac{9}{1} ,\pm \frac{18}{1} \)

and also,

\(\large \pm \frac{1}{2} , \pm \frac{2}{2} ,\pm \frac{3}{2} ,\pm \frac{6}{2} ,\pm \frac{9}{2} ,\pm \frac{18}{2} \)

Answer 10

simplify the fractions, and remove any duplicates

Answer 11

oh ok. thank you!

Answer 12

that was really helpful!

Answer 13

np :) glad it helped !