Let $f(x)=12x^3-32x^2+25x-6$ Find analytical $r,s \in \mathbb{Q}, r<s$ such that $f(r)=f(s)$

Question

Help with this excercise..

Let $$f(x)=12x^3-32x^2+25x-6$$ Find analytical $r,s \in \mathbb{Q}, r<s$ such that $f(r)=f(s)$ and it proof that $f$ is not injective..

Answer 1

I would simply find the roots. For example, note that $r=1/2$ and $s = 3/2$ are such that $r<s$ and $f(r)=f(s)=0.$