If the solutions of f(x)=0 are 1 and -2, then the solutions of f(2x)=0 are
a)1 and 2
b) 1/2 and -1
c) 2 and -4
d)-2 and 4
2)-1/2 and -1
If the solutions are 1 and -2, and assuming f(x) is a polynomial, then
f(x)=k(x-1)(x+2)
and
f(2x) = k(2x-1)(2x+2)
implying
2x-1=0 or (2x+2)=0
Solve for x.
To find the solutions of the equation f(2x) = 0, we need to substitute 2x into the function f(x) and solve for x.
Given that the solutions of f(x) = 0 are 1 and -2, we can set up the equation as follows:
f(2x) = 0
f(x) = 0 by substituting 2x for x
Now, we need to find the values of x such that f(x) = 0.
Since we know that the solutions of f(x) = 0 are 1 and -2, we can substitute these values into the equation f(x) = 0 to find the corresponding values of x:
For f(1) = 0:
f(1) = 0 if and only if x = 1
For f(-2) = 0:
f(-2) = 0 if and only if x = -2
Now, let's substitute 2x into the equation f(x) = 0:
For f(2x) = 0:
f(2x) = 0 if and only if 2x = 1 or 2x = -2
To solve for x, we divide both sides of each equation by 2:
For 2x = 1:
x = 1/2
For 2x = -2:
x = -1
Therefore, the solutions of f(2x) = 0 are x = 1/2 and x = -1.
The correct answer is option (b) 1/2 and -1.