Answer:
Using the Rational Root Theorem, the possible rational roots of 5x^3+6x^2-9x+2=0 are ±1, ±2, ±1/5, and ±2/5.
By testing these values, we find that x=-2/5 is a root. Using synthetic division, we can then factor out (5x+2) from the polynomial:
5x^3+6x^2-9x+2 = (5x+2)(x^2+x-1)
The remaining quadratic factor can be factored using the quadratic formula or by completing the square:
x^2+x-1 = 0
x = (-1 ± sqrt(5))/2
Therefore, the zeros/rational roots of the polynomial are x=-2/5, x=(-1+sqrt(5))/2, and x=(-1-sqrt(5))/2.