Question

How many x intercepts appear on the graph of this polynomial function?

f(x) = x^4 - 5x^2
A) 1 x intercept
B) 2 x intercepts
C) 3 x intercepts
D) 4 x intercepts

Answer 1

Option C -3 x-intercept

Explanation:

Given : Polynomial function
`f(x) = x^4 - 5x^2`

To find : How many x intercepts appear on the graph of this polynomial function?

Solution :

To find the x-intercept we put y equals to zero.

Let
`y= x^4 - 5x^2`

Now, Substitute y=0

`0= x^4 - 5x^2`

We solve for x,

`x^2(x^2-5)=0`

`\text{ Either }x^2=0\text{ or } x^2-5=0`

`\text{ Either }x=0\text{ or } x^2=5`

`\text{ Either }x=0\text{ or } x=\pm√(5)`

So,
`x=0,\sqrt5,-√(5)`

Which means there are three x-intercept.

Therefore, Option C is correct.