Question

If a continuous function 𝑓(𝑥) does not have a root in the interval [𝑎,𝑏], then which one of the following statements is TRUE?
(A) 𝑓(𝑎)⋅𝑓(𝑏)=0
(B) 𝑓(𝑎)⋅𝑓(𝑏)<0
(C) 𝑓(𝑎)⋅𝑓(𝑏)>0
(D) 𝑓(𝑎)/𝑓(𝑏)≤0

Answer 1

can i help u

Answer 2

yes please

Answer 3

ok then let me see

Answer 4

have u got the answer??

Answer 5

uhh hold on i got caught up

Answer 6

k..

Answer 7

im confused now

Answer 8

i would say its b but dont go with what i say

Answer 9

i think its b tho

Answer 10

any explanation for u r answer

Answer 11

the fact that B seems like it can be greater than 0 and not less than zero

Answer 12

so u r telling option C might be the answer

Answer 13

yes

Answer 14

if f(a) and f(b) in opposite signs, then we can get the value less than zero.. what do u say??

Answer 15

i say it would be a different answer than because if they r opposite wouldn't that take us back to choice b

Answer 16

i have made 3 analysis for this question... these three will give me 3 other results which matches all the options.. so i'm confused, which one is correct

Answer 17

B i think its B

Answer 18

why u wanna no

Answer 19

it will be helpful for me.. in asking questions

Answer 20

uh im from connections academy

Answer 21

sorry.. i did not get.. will u be still more clear

Answer 22

i come from chicago

Answer 23

u r education.

Answer 24

yeah im educated why

Answer 25

y r u asking these questions

Answer 26

oh idk no all i know is that im doing math thats it

Answer 27

k.. thanks for u r answer... i'll find out correct one by some other means

Answer 28

f(a) and f(b) cannot have opposite signs if there is no root in {a,b]

Answer 29

so which option follows from that?

Answer 30

u r answer

Answer 31

think about it - f(a) and f(b) are either both positive or both negative.

Answer 32

)so their product f(a) * f(b) must be what?

Answer 33

greater than zero.. but if f(a) is at zero then we get zero as answer

Answer 34

if f(a) is a zero then tha'ts a root.

Answer 35

how?

Answer 36

So C

Answer 37

thats the definition of a root - sometimes its called a zero.

Answer 38

in particular root need not be a zero

Answer 39

No i'm not saying the root is zero The root of a function is sometimes called the zero of the function - thats more usual in the US - not so much in the UK.

Answer 40

could u explain in detail????????

Answer 41

Lets try a graph
in following graph f(a) and f(b) are both positive and there are no roots (because the graph does not pass through the x-axis)