Question

Find The Zeros Of the function f(x) 3x^4 - 24x

Answer 1

Given:

The given function is
`f(x)=3x^4-24x`

We need to determine the zeros of the function.

Zeros of the function:

The zeros of the function are the values that makes the function's value equal to zero.

The zero of the function can be determined by substituting f(x) = 0 in the function.

Thus, we have;

`0=3x^4-24x`

Switch sides, we get;

`3x^4-24x=0`

Let us factor out the common term 3x.

Thus, we have;

`3x(x^3-8)=0`

`3x(x^3-2^3)=0`

Using the identity,
`x^(3)-y^(3)=(x-y)\left(x^(2)+x y+y^(2)\right)`, we get;

`3 x(x-2)\left(x^(2)+2 x+4\right)=0`

Let us solve using the zero factor principle.

Thus, we have;

If
`3x=0` then
`x=0`

If
`x-2=0` then
`x=2`

If
`x^2+2x+4=0` then
`x=-1+√(3) i, x=-1-√(3) i` (solving using the quadratic formula)

Thus, the zeros of the function are
`x=0, x=2, x=-1+√(3) i, x=-1-√(3) i`