Question

What are the zeros of the polynomial function: f(x) = (x + 4)(2x – 1)(x – 7)?

Answer 1

well it's already factored, just set each one equal to zero:
x+4=0
2x-1=0
x-7=0

Answer 2

Each factor needs to be zero.

So that means:

x - 4 = 0

x = 4

2x - 1 = 0
2x = 1
x = 1/2

x + 7 = 0
x = -7
Does that help?

Answer 3

okkk
so its -4,1/2,and 7 ?

Answer 4

yup :)
MK messed up

Answer 5

Crap I did just noticed sorry @Lesha

Answer 6

its okk (: . you still helped me understand the concept
Which of the following represent the zeros of f(x) = 6x3 – 31x2 + 4x + 5 ?
how do i find this one ?

Answer 7

mistakes happen ^_^'

Answer 8

I think
f(5) = 6*125 - 31*25 + 4*5 + 5
= 750 - 775 + 20 + 5
= 0
f(-1/3) = -6/27 - 31/9 - 4/3 + 5
= -2/9 - 31/9 - 4/3 + 5
= 0
f(1/2) = 6/8 - 31/4 + 4/2 + 5
= 3/4 - 31/4 + 2 + 5
= 0
So the zeros are 5, -1/3, and 1/2.

Answer 9

Hope thats right

Answer 10

How did you get those? @MKTY

Answer 11

What are the zeros of the polynomial function: f(x) = x3 + 2x2 – 24x ?

–6, 0, 4

Answer 12

is that right ?

Answer 13

Yes, that's right :P

Answer 14

(;;;;
What are the possible number of positive, negative, and complex zeros of f(x) = 3x4 – 5x3 – x2 – 8x + 4 ?

Answer 15

sign changes

Answer 16

do step by step

Answer 17

2

Answer 18

step by step

Answer 19

step1 : f(x) sign changes
step2 : f(-x) sign changes

Answer 20

2
then 3 ?

Answer 21

2 for f(x) is correct, so that gives a positive zeroes of : 2 or 0

Answer 22

3 for f(-x) is wrong, try again

Answer 23

f(x) = = 3x4 – 5x3 – x2 – 8x + 4

f(-x) = 3x4 + 5x3 - x2 + 8x + 4

how many sign changes ?

Answer 24

ummm 2. how do you know what to chhange it to ?

Answer 25

good q :) lets work on it a bit

Answer 26

f(x) = = 3x4 – 5x3 – x2 – 8x + 4


for f(-x), u just replace x with -x everywhere

Answer 27

replace and see wat u get

Answer 28

like this
1f(x) = = -3x4 – 5x3 +x2 – 8x - 4
? soorryy im confused

Answer 29

not exactly, just replace x with -x first :-

\(3x^4 – 5x^3 – x^2 – 8x + 4 \)

\(3(-x)^4 – 5(-x)^3 – (-x)^2 – 8(-x) + 4 \)

Answer 30

okk i get it. so now whats the next step.

Answer 31

u get how to figure out f(-x) ?

Answer 32

yess i dooo nowww.

Answer 33

great !

Answer 34

once we knw number of sign changes in f(x) and f(-x), here is how we conclude :-

Answer 35

2 sign changes in f(x) . so number of positive zeroes = 2, or 0
2 sign changes in f(-x) . so number of negative zeroes = 2, or 0
Number of complex zeroes : 4, 2, or 0

Answer 36

According to The Fundamental Theorem of Algebra, how many zeros does the function f(x) = 15x23 + 41x19 + 13x5– 10 have ?

Answer 37

what does "Fundamental Theorem of Algebra" say ?