Question

Im needing help please Find all real zeros of the function Please see attached picture

Answer 1

We must find the zeros of the following function:

`f(x)=4\cdot(x+3)^2\cdot(x-3)\cdot(x^2-49).`

Now, the zeros of a function are the values of x when f(x) is equal to 0. So we must find all the values of x that makes f(x) = 0. To do that, it is convenient to rewrite the function f(x) as:

`f(x)=4\cdot(x+3)\cdot(x+3)\cdot(x-3)\cdot(x+7)\cdot(x-7)\text{.}`

Where we use the fact that:

• (x + 3)² = (x + 3) (x + 3),

,

• (x² + 49) = (x + 7) (x - 7).

From the previous equation, we see that if we replace x with the following values, we get f(x) = 0:

• x = -3,

,

• x = 3,

,

• x = -7,

,

• x = 7.

Answer

All the real zeros of the function are -3, 3, -7, 7.