Zeros of a Function?

Question

I was wondering if their was any advice or tricks/ways to find zeros without graphing capabilities/a calculator...

not all can be solved easily by just setting y=0...

PLEASE HELP WITH THIS EXAMPLE:

how would you find the zeros of y=(j)^3 - 7(j) + 6

Answer 1

by uisng factor theorem and rational root test

by rational root test

y=(j)^3 - 7(j) + 6

has rational roots then it has to be factor of 6 that is +/-1, or +/-2 or +/-3 or +/-6

if we put j =1 we get y = 1-7+6 -0

so j-1 is a factor

j^3-7j + 6

= j^3-j- 6j +6

= j(j^2-1) -6(j-1)

= (j-1)(j^2+j-6)

now  j^2+j-6 is quadatic and factored as (j+3)(j-2)

so zeroes are 1 -3 and 2