SOLUTION: Suppose the zeros of a given function f are -1,2, and 5. a. What are the zeros of the function g(x)=2f(x)? b. What are the zeros of the function h(x)=f(2x)

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Suppose the zeros of a given function f are -1,2, and 5. a. What are the zeros of the function g(x)=2f(x)? b. What are the zeros of the function h(x)=f(2x)      Log On


   

Question 1046439: Suppose the zeros of a given function f are -1,2, and 5.
a. What are the zeros of the function g(x)=2f(x)?
b. What are the zeros of the function h(x)=f(2x)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the zeros of a given function f are
x%5B1%5D=+-1,
x%5B2%5D=2, and
x%5B3%5D=5
use zero product theorem to find f%28x%29
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29
f%28x%29=%28x-%28-1%29%29%28x-2%29%28x-5%29
f%28x%29=%28x%2B1%29%28x-2%29%28x-5%29
f%28x%29=%28x%2B1%29%28x-2%29%28x-5%29
f%28x%29=x%5E3-6x%5E2%2B3x%2B10
a. What are the zeros of the function g%28x%29=2f%28x%29?
use factored form f%28x%29=%28x%2B1%29%28x-2%29%28x-5%29
g%28x%29=2%28%28x%2B1%29%28x-2%29%28x-5%29%29
0+=+2+%28x-5%29+%28x-2%29+%28x%2B1%29...basically nothing will change
the zeros of a function g%28x%29 are same as of a +f%28x%29
x%5B1%5D=+-1,
x%5B2%5D=2, and
x%5B3%5D=5
b. What are the zeros of the function h%28x%29=f%282x%29+
if f%28x%29=x%5E3-6x%5E2%2B3x%2B10, then
h%28x%29=f%282x%29+=%282x%29%5E3-6+%282x%29%5E2%2B3+%282x%29%2B10
h%28x%29+=8x%5E3-24x%5E2%2B6x%2B10
h%28x%29++=+2%282x%2B1%29%282x-5%29%28x-1%29
2%282x%2B1%29+%282+x-5%29+%28x-1%29=0
if 2+%282x%2B1%29+=0, then %282x%2B1%29+=0-> and x+=-1%2F2
if %282+x-5%29+=0%7B%7B%7B-%3E+then+%7B%7B%7B2x=5-> and x=5%2F2
if %28x-1%29=0-> x=1