ANSWER
The zeros are [tex]x=-5,x=0,x=5[/tex]
EXPLANATION
Given;
[tex]f(x)=x^4-25x^2[/tex].
We can rewrite the function as
[tex]f(x)=x^2(x^2-25)[/tex]
[tex]\Rightarrow f(x)=x^2(x^2-5^2)[/tex]
[tex]\Rightarrow f(x)=x^2(x-5)(x+5)[/tex]
The zeros are found by equating the function to zero.
[tex]\Rightarrow x^2(x-5)(x+5)=0[/tex]
[tex]\Rightarrow (x-5)=0[/tex]
The multiplicity is 1, since it is odd the graph crosses at this intercept. which is [tex]x=5[/tex]
Or
[tex]\Rightarrow (x+5)=0[/tex]
The multiplicity is 1, since it is odd the graph crosses at this intercept. which is [tex]x=-5[/tex]
Or
[tex]\Rightarrow x^2=0[/tex]
This last root has a multiplicity of 2.
That is
[tex]x=0[/tex] repeats two times.
Since the multiplicity is even, the graph touches the x-axis at the point [tex]x=0[/tex].
See graph.
