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

Answer:

Option C -3 x-intercept

Step-by-step 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,

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

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

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

$\text{ Either }x=0\text{ or } x=\pm\sqrt{5}$

So, $x=0,\sqrt5,-\sqrt{5}$

Which means there are three x-intercept.

Therefore, Option C is correct.