Question

Find all zeros.

f(x) = x( x + 2 )( x - 2)( 3^2 - 4)

Answer 1

>f(x) = x( x + 2 )( x - 2)( 3^2 - 4)

Is the last factor supposed to be ( x^2 - 4) rather than ( 3^2 - 4) as shown in the problem?

Answer 2

the last factor is 3 to the second power subtract 4.

Answer 3

Zeros are x-intercepts. To get on the x-axis, y must be zero. That means f(x) = 0

0 = x( x + 2 )( x - 2)( 3^2 - 4)

By the Zero Product Property, if you get a product of zero, then one or more of the factors is equal to zero.

Answer 4

0 = x( x + 2 )( x - 2)( 3^2 - 4)

0 = x
OR
(x + 2 ) = 0
Or
(x - 2) = 0
Or
( 3^2 - 4) = 0

Solve each of those for x to get the zeros.

Answer 5

thank you very much!

Answer 6

You are welcome.

What did you get for the answers?

Answer 7

i got 3 possible zeros.
-2 , 2, 4^2 / 3^2 or 2 and the square root of three over 9... i think that's right, please check and if it's wrong please correct it.

Answer 8

3 zeros, yes. Get them from the equations.

I got x = 0, x = - 2, and x = 2. That's all.

Answer 9

4^2 / 3^2 or 2 and the square root of three over 9 is a mystery answer.

( 3^2 - 4) = 0 leads nowhere because ( 9 - 4) = 5 which does not equal 0.

That is why I asked you early on if that 3^2 was supposed to be x^2. You said no.

So, it's a constant term and never equal to 0 in this problem.

Answer 10

oh okay i see what i did wrong! thank you very much! have a great day or night ^_^

Answer 11

You are welcome.