The number of distinct real roots of $x^4-4x^3+12x^2+x-1=0$ is

Let $f\left(x\right)=x^4-4x^3+12x^2+x-1$

$\begin{array}{l}\therefore f^{\mathrm{\prime }}\left(x\right)=4x^3-12x^2+24x+1\\ \Rightarrow f^{\prime \prime }\left(x\right)=12x^2-24x+24\\ =12\left(x^2-2x+2\right)\\ =12\left[(x-1{)}^2+1\right]>0\end{array}$

i.e, $f^{\prime \prime }\left(x\right)$  has no real roots

Hence, $f\left(x\right)$  has maximum two distinct real roots, where 

$f\left(0\right)=-1$