The number of values of ‘a’ for which $(a^2-3a+2)x^2+(a^2-5a+6)x+a^2-4=0$ is an identity in ‘x’ is

$(a^2-3a+2)x^2+(a^2-5a+6)x+a^2-4=0$ is an identity

$\begin{array}{lll}{a}^2-3a+2=0& a^2-5a+6=0& a^2-4=0\\ a^2-2a-a+2=0& a^2-2a-3a+6=0& (a+2)(a-2)=0\\ a(a-2)-1(a-2)=0& a(a-2)-3(a-2)=0& a=2,-2\\ a=1,a=2& a=2,a=3& \end{array}$

In three cases common value $a=2$

$\therefore$ Number of values of a is 1.