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

Answer:

E. -2, 4

Step-by-step 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.

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

So, the zeroes are -2, 4.