Question

What are the possible rational zeros of f(x) = x4 + 2x3 – 3x2 – 4x + 18 ?

Answer 1

± 1, ± 2, ± 3, ± 6, ± 9, ± 18
is it ?

Answer 2

are u doing the method where u sub in one of those numbers and see which one works

Answer 3

noo i didnt do that

Answer 4

thats right !

Answer 5

Yayyy (:

Answer 6

good work :)

Answer 7

... you have x^4 and yet you have 6 possible answers...???

Answer 8

Jack, not 6, there are 12 possible answers. that too oly rational zeroes

Answer 9

12* possible answers actually but ya ^^ what he said

Answer 10

these are the numbers that shes gotta try to sub in to see which one works and then do the whole synthetic division BS i hate it

Answer 11

isnt there a quicker way to find the roots of this equation

Answer 12

we dont need to find zeroes

Answer 13

just asking in general

Answer 14

question is not about finding zeroes

Answer 15

ohk...

Answer 16

If f(x) = 3x – 1 and g(x) = x2 – 2x – 2, what is f(g(x))
how would i do this ?

Answer 17

take f(x)

replace x wid g(x)

Answer 18

f(x) = 3x – 1

f(g(x)) = 3(g(x)) - 1

Answer 19

now replace g(x) wid x2 - 2x - 2

Answer 20

f(g(x)) = 3(x2 - 2x - 2)) - 1

Answer 21

f(x) = 3x – 1

f(g(x)) = 3(g(x)) - 1

= 3(x2 - 2x - 2) - 1

Answer 22

good :) simplify

Answer 23

sorry, get it now, "possible answers", thought that meant solve fo y=0
my bad cheers @ganeshie8 @dan815

Answer 24

aha jack got u :)

Answer 25

3x²-6x-6-1

Answer 26

simplify more

Answer 27

lol u want to leave -6-1 like that ha

Answer 28

3x²-6x-7

Answer 29

lol right now ?

Answer 30

looks good :)

Answer 31

What are the possible number of positive, negative, and complex zeros of f(x) = –x6 – x5– x4 – 4x3 – 12x2 + 12 ?

Answer 32

Descartes rules of signs, heard of that right ?

Answer 33

Yess. but im not sure how to do it .

Answer 34

f(x) = –x6 – x5– x4 – 4x3 – 12x2 + 12

step1 : find number of sign changes in f(x)

Answer 35

1 ?

Answer 36

Yes, so number of positive zeroes = 1 ------------------(1)

Answer 37

step2 : find number of sign changes in f(\(\color{red}{-}\)x)

Answer 38

f(x) = –x6 – x5– x4 – 4x3 – 12x2 + 12

f(-x) = ?

Answer 39

umm 6 ? im not sure how to do that part.

Answer 40

first find f(-x) and then we can simply count

Answer 41

f(x) = –x6 – x5– x4 – 4x3 – 12x2 + 12

f(-x)= -x6 + x5 -x4 + 4x3 - 12x2 + 12

Answer 42

how many sign changes in f(-x) ?

Answer 43

ohh ok soo 5 ?

Answer 44

Yes, 5 changes so, we can have 5, 3, or 1 negative zeroes

Answer 45

so its Positive: 1; Negative: 5, 3, or 1; Complex: 4, 2, or 0

Answer 46

so, number of negative zeroes = 5, 3, or 1 ------------------(2)

Answer 47

brilliant ! thats it !!!

Answer 48

(;;. Yayyy !

Answer 49

very good work as usual :)