How can you find this real zeros?

Question

Find all real zeros of the function to the nearest 0.001.
f(x)=x^3-x+6. Thank you so much. I appreciated it.

Answer 1

First check for rational zeros.
Any rational zero must divide 6
and by trial we find that -2 is a zero.
That means x+2 is a factor of x^3-x+6.
By long division or synthetic division,
the quotient is x²-2x+3.
But the discriminant of x²-2x+3 is 4-12 = -8
so the quotient has no real zeros.
So the only real zero is x = -2.

Answer 2

I think maybe some geniuses will know about this question.