The equation whose roots are smaller by 1 than those of $2x^2-5x+6=0$ is

Let $\alpha$ is a root of $2x^2-5x+6=0$

Let $\alpha -1=x$

$\Rightarrow \alpha =x+1$

But $\alpha$ is a root of $f\left(x\right)$

$$\begin{gathered} \Rightarrow f\left(\alpha \right)=0 \\ \Rightarrow f(x+1)=0 \\ \Rightarrow 2{(x+1)}^2-5(x+1)+6=0 \\ \Rightarrow 2(x^2+1+2x)-5x-5+6=0 \\ \Rightarrow 2x^2+2+4x-5x-5+6=0 \\ \Rightarrow 2x^2-x+3=0 \end{gathered}$$