Is my work for this problem correct?

Question

Directions: State the possible rational zeros for each function.
Question: f(x) = 3x^2 + 2x – 1
Answer:
Constant term:-1 Factors: 1
Leading coefficient:3 Factors: 1 and 3
±1/1,3= ±1/1,3 and ±1/1,3
= ±1/1 and ±1/3
= ±1 and ±1/3

Answer 1

I don't think so, lets look

3x^2+2x-1=0
x^2+2/3 x =1
x^2+2/3 x +1/9=10/9
(x+1/3)^2= 10/9
x+1/3 = +- 1/3 sqrt 10

x=-1/3 +- 1/3 sqrt10

check that.

Answer 2

Bob, in line #2 , you forgot to divide the 1 by 3

it actually factors into
(x+1)(3x-1) = 0

so x = -1 or x = 1/3