Question

If \(\LARGE{\color{red}{f(x)=ax^2+bx+c}}\). Which one of the following is true :-

a. \(\LARGE{f(x_1/x_2)=f(x_1)f(x_2)}\)
b. \(\LARGE{f(x_1+x_2)=f(x_1)+f(x_2)}\)
c. \(\LARGE{f(x_1/x_2)=f(x_1)/f(x_2)}\)
d. none of these.

Answer 1

@hartnn @mathslover @satellite73 plz help :)

Answer 2

& explain with reason :)

Answer 3

Try plugging it in.

Answer 4

\[\Large
f(x_1/x_2)=a(x_1/x_2)^2+b(x_1/x_2) +c
\]Simplify can see where it goes.

Answer 5

If you cant get it in the form of: \[ \Large
f(x_1)f(x_2) = [a(x_1)^2+b(x_1)+c] [a(x_2)^2+b(x_2)+c]
\]Then it is true.

Answer 6

It might actually be better to try going backwards.

Answer 7

if you CAN get it in the form^

Answer 8

@jiteshmeghwal9 Does it make sense?

Answer 9

Dude, i'm totally confused :(

Answer 10

I must try this a bit later well u did ur best :)

Answer 11

u deserve a medal for all this stuff :)

Answer 12

I can give you a hint.

Consider what happens to \(c\).

Answer 13

Or even better, try doing \(x_1 = 0\) and \(x_2=1\)
See if it holds true. If it doesn't, you have a counter example.
So you know it would be false.