$Thenumberofvaluesofaforwhich(a^2-3a+2)x^2+(a^2-5a+6)x+a^2-4=0isanidentityinxis$

$\begin{array}{l}GivenEquation(a^2-3a+2)x^2+(a^2-5a+6)x+(a^2-4)=0\\ isanidentityifallitscoefficients\\ areequaltozerosimul\tan eously\\ \therefore a^2-3a+2=0\Rightarrow (a-2)(a-1)=0\Rightarrow a=1,2\\ and{a}^2-5a+6=0\Rightarrow (a-2)(a-3)=0\Rightarrow a=2,3\\ and{a}^2-4=0\Rightarrow (a+2)(a-2)=0\Rightarrow a=\pm 2\\ coefficientsareequaltozero\\ simulaneouslywhena=2\\ \therefore Onlyonevalueof\text{'}a\text{'}.\end{array}$