Question

Graph the function f(x) = x3 – 4x – 1. Which are approximate solutions for x when f(x) = 0?

Answer 1

if f(x) is = to 0 then that means that you would have to plug the 0 in for all of the x that are in the function and the solve it.
f(x)= x3-4x-1
f(0)= (0)3-4(0)-1
0 0 0 -1
-1
so that means that -1 would be the answer for the function

Answer 2

x = 1, √5, -√5

Explanation:

Graphing of Function:

The given function will cut the y-axis at (0,-1) and it will cut the x-axis at (0,1),(0,√5), (0.-√5).

We are given the function f(x) =
`x^3 - 4x - 1 = 0`

We have to approximate the solutions when f(x) = 0, that is,

f(x) =
`x^3 - 4x - 1 = 0` = 0

⇒
`x^3 - 4x = 1`

⇒
`x(x^2 - 4) = 1`

⇒ x = 1,
`x^2 - 4 = 1`

Now,
`x^2 - 4 = 1`

⇒
`x^2 = 5`

⇒ x = ±√5

Thus, x = 1, √5, -√5