Question

List all the possible rational zeros of
f(x)=3x^3-x^2+2x=2.

Please help me. I don't understand how to do this. Can someone show me please.

Answer 1

If a polynomial f(x)=0 has rational roots, the numerator must be a factor of the constant term, and the denominator must be a factor of the highest-power coefficient.

so, since you have f(x) = 3x^3-x^2+2x+2

any rational roots must have a numerator which divides 2, and a denominator which divides 3. So, any rational root must be in the list

±1/1, ±2/1, ±1/3, ±2/3

This comes from the fact that if you have (in this case) 3 roots (p,q,r) for

f(x) = ax^3 + bx^2 + cx + d

pqr = -d/a
pq + pr + qr = c/a
p + q + r = -b/a