Question

the roots of the equation f(x)=0 are 1 and -2. The roots of f(2x)=0 are....

A. 1 and -2
B. 1/2 and -1
C. -1/2 and 1
D. 2 and -4
E. -2 and 4

Answer 1

Roots mean for what values of x make f(x) zero. They give you that when x =1 or x=-2 that f(x) = 0. This means that f(1)=0 and f(-2)=0. If f(x) = x-1, then if x=1, f(x)=0. Do you see why?

Answer 2

So would the answer be C? @ybarrap

Answer 3

No. Why do you think that?

Answer 4

We haven't dealt with f(2x) yet. We only know if f(x)=x-1, then f(1)=0. We still need to add another team to make this same function equal zero at negative 2. That would be if f(x)=(x+2). Now how do we combine these two results so that f(1)=0 and f(2)=0? Once we're done with that, we can set y=2x to find f(y)=0 and immediately get our answer.

Answer 5

f(x)=(x-1)(x+2)

Does this satisfy f(1)=f(-2)=0?

Answer 6

Yes!!

Answer 7

But we need f(2x). This is easy now. f(2x)=(2x-1)(2x+2)=0. What values of x make this true?

Answer 8

x=1/2 and x=-1

Answer 9

Perfect!

Answer 10

Thanks!!!

Answer 11

yw