Question

What are the possible numbers of positive, negative, and complex zeros of f(x) = -3x^4 + 5x^3 - x^2 + 8x + 4?

Answer 1

@satellite73

Answer 2

fractions where the numerator divides 4 and the denominator divides 3

Answer 3

there are a few of those

Answer 4

the 8x and 4?

Answer 5

divisors of 4 are
\[\pm1,\pm2,\pm4\] so do the same with a 3 in the denominator

Answer 6

ignore everything but the 4 at the end and the 3 at the beginning

Answer 7

k so since you already found the 4 all i gotta do is the -3x^4?

Answer 8

the others are
\[\pm\frac{1}{3}\] and so on

Answer 9

do you want to see the answer choices?

Answer 10

no

Answer 11

i don't know how to do this im not sure what you mean by 3 as the denominator like do you want any fraction with 3 as the denominator ?

Answer 12

\[\pm \frac{1}{3},\pm \frac{2}{3},\pm\frac{4}{3}\]

Answer 13

got it?

Answer 14

yeah so like [\pm\frac{ 6 }{ 3 }\] would that work?

Answer 15

\[\pm \frac{ 6 }{ 3 }\]

Answer 16

lol just the ones i wrote
the top as to divide 4

Answer 17

okay so i devide all those by 4 or what?

Answer 18

let me write them out for you ok?

Answer 19

ok

Answer 20

\[\pm1,\pm2,\pm4\pm \frac{1}{3},\pm \frac{2}{3},\pm\frac{4}{3}\]

Answer 21

top goes in to 4, bottom goes in to 3

Answer 22

ohhh i see what you mean like the numerator goes into 4 and he denominator goes into 3?

Answer 23

yay

Answer 24

but thats not one of the answer choices

Answer 25

oooh i see

Answer 26

crap we have to use descartes rule of sign

Answer 27

\[ f(x) = -3x^4 + 5x^3 - x^2 + 8x + 4\] has 3 changes in sign
from -3 to +5, from +5 to -1, from -1 to +8

Answer 28

so there are either 3 positive zeros, or one positive zero
(you count down by twos)

Answer 29

\[f(-x) = -3x^4 - 5x^3 - x^2 - 8x + 4\] has one change in sign from -8 to +4

Answer 30

i thought 0 was a nutreul number? not negative nor positive?

Answer 31

changes in sign of the coefficients
yes, zero is not negative or positive, we are counting the roots

Answer 32

oh okay

Answer 33

Positive: 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0
Positive: 1; negative: 3 or 1; complex: 2 or 0
Positive: 3 or 1; negative: 1; complex: 2 or 0 <--- s this the answeR?
Positive: 4 or 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0

Answer 34

well we don't have to do much work because only one choice starts with positive zeros 3 or 1

Answer 35

yeah C as you picked

Answer 36

thank you i got a whole bunch more btw Xd