f(x)=7x³+x²+7x-1

That is not factorable, so I suspect there is a typo and it 
should have been either

f(x)=7x³-x²+7x-1  or f(x)=7x³+x²-7x-1 or f(x)=7x³+x²+7x+1

because all those are factorable by grouping, whereas the
one given is not.

If it should have been

f(x)=7x³-x²+7x-1

Factor the first two terms by taking out x²

f(x)=x²(7x-1)+7x-1

Factor 1 out of the last two terms

f(x)=x²(7x-1)+1(7x-1)

Now factor out (7x-1)

f(x)=(7x-1)(x²+1)

That's in factored form

To find the zeros set each factor = 0

7x-1 =9
  7x = 1
   x = .  That's one zero.

x²+1 = 0
  x² = -1
   x = ±i

So the three zeros are , i and -i.

If it was one of the others, they're all just 
like this one except for + and - signs.

Edwin