Question

Given a function f(x).
Find at least one root of the equation f(x) = f(a)

Answer 1

x=a?

Answer 2

hm yaa:)
but how?

Answer 3

let f(x) = x+3

so f(x) = f(a) --> given

f(a) = a+3

x+3=a+3
x=a

Answer 4

I don't know whether I am right or wrong..

Answer 5

oh ok!
but is there any use of remainder theorem?

Answer 6

yes wait lemme think

Answer 7

ok:)

Answer 8

r u sure that i am right with x = a?

Answer 9

yeah
this answer is also given in my book:D

Answer 10

ok so i got it right

so lemme give you explanation with remainder theorem

Answer 11

ok:)

Answer 12

I do have remainder = 0

u agree?

Answer 13

if i divide f(x) / f(a) then remainder =0

Answer 14

?

Answer 15

sorry i didn't gt u:(

Answer 16

given f(x) = f(a)

f(x) = f(a) * 1
f(x)/f(a) = 1

this means if we divide f(x) by f(a) the remainder = 0

Answer 17

@mathslover where did u get 3

Answer 18

how did u get this?
divide f(x) / f(a) then remainder =0

Answer 19

since f(x) = f(a)

what is the remainder when x-3 is divided by x-3 @maheshmeghwal9 ?

Answer 20

0.

Answer 21

good

so if we dvide f(x) by f(a)

we get remainder = 0 right?

Answer 22

since f(x)=f(a)

hence f(x)/f(a) = f(x)/f(x) => remainder = 0

Answer 23

ya right:)

Answer 24

oh ok i gt it:)
thanx @mathslover :D

Answer 25

so f(a) is the factor of f(x)

Answer 26

that is x-a is a factor of f(x)

Answer 27

hence x-a = remainder
x-a= 0
x=a

proved

Answer 28

:)
thanx:)

Answer 29

no problem and best of luck

Answer 30

stu:)

Answer 31

stu ?

Answer 32

what does that mean @maheshmeghwal9

Answer 33

@mathslover
sorry for wait reply.
actually
stu = same to u:D