Question

If the zeros of f(x) are x=-1 and x=2, then the zeros of f(x/2) are

A. -1, 2
B. -1/2, 5/2
C. -3/2, 3/2
D. -1/2, 1
E. -2/4

Answer 1

E. -2, 4

Explanation:

If the zeroes of a function are given as
`\alpha, \beta`, then the function can be written as:

`(x-\alpha)(x-\beta) = 0`

Here, we are given that zeros of
`f(x)` are x=-1 and x=2.

As per above, we can write the function
`f(x)` as:

`(x- (-1))(x-2) = 0\\\Rightarrow (x+1)(x-2)=0`

So,
`f(x) =(x+1) (x-2)`

To find:

Zeroes of
`f(\frac{x}2)`.

Solution:

We have found that
`f(x) =(x+1) (x-2)`

Replacing
`x` with
`\frac{x}2`:

`f(\frac{x}2) =(\frac{x}2+1) (\frac{x}2-2)`

Now, Let us put it equal to 0 to find the zeroes.

`f(\frac{x}2) =(\frac{x}2+1) (\frac{x}2-2) = 0\\\Rightarrow (\frac{x}2+1) = 0 \ OR\ (\frac{x}2-2) =0\\\Rightarrow (x)/(2) = -1\ OR\ (x)/(2)=2\\\Rightarrow \bold{x =-2, 4}`

So, the zeroes are -2, 4.