Answer:
Step-by-step explanation:
it is of 7 degree so number of zeros is 7
f(x)=x^4-x^7=x^4(1-x³)=x^4(1-x)(1+x+x²)
x^4=0,gives x=0,0,0,0
so four zeros are repeated.
So x=0 is repeated four times.
1-x=0,gives 1-x=0,x=1
1+x+x²=0
x²+x+1/4=-1+1/4=-3/4
(x+1/2)²=-3/4==((√3) \iota/2)²
x+1/2=±(√3\iota)/2
x=-1/2±(\iota√3)/2
[tex]x=\frac{-1 \pm\sqrt{3} \iota }{2} \\so ~x=\frac{-1+\sqrt{3} \iota }{2} \\and~x=\frac{-1-\sqrt{3} \iota }{2} \\[/tex][tex]these~roots~are~imaginary.\\only ~x=0,1~are~real.[/tex]
