ANSWER
x = 0 and x = 1
EXPLANATION
In the given function
[tex]f(x)=x^7-x^4[/tex]We can see clearly that one of the zeros is x = 0. Note that x is in all the terms of the polynomial, so whenever x is zero, the value of the function is zero.
According to the degree of this polynomial we should find 7 zeros. However, as we can see there are only two terms in this function and they all have x. Therefore, it is likely that the some of the zeros have a multiplicity greater than 1.
For x = 0, if we take x⁴ as a common factor:
[tex]f(x)=x^4(x^3-1)[/tex]We can see that the multiplicity of this zero is 4.
Another zero is found by solving:
[tex]x^3-1=0[/tex]Add 1 to both sides of the equation:
[tex]\begin{gathered} x^3-1+1=0+1 \\ x^3=1 \end{gathered}[/tex]And take cubic root:
[tex]\begin{gathered} \sqrt[3]{x^3}=\sqrt[3]{1} \\ x=1 \end{gathered}[/tex]The other zero is x = 1, with multiplicity 3.
Since 4+3=7, we have found all the zeros of this function.
