Statement-1: The number of values of a for which $\left(a^2-3 a+2\right) x^2+\left(a^2-5 a+6\right)

Question

Statement-1: The number of values of a for which $\left(a^2-3 a+2ight) x^2+\left(a^2-5 a+6ight) x+a^2-4=0$ is an identity in $x$ is 2 \Statement-2: If $a=b=c=0$ then equation $a x^2+b x+c=0$ is an identity in $x$.

Professor PC Thomas Classes · Answer

Identity means it should be satisfied for all values of $x$. $a^{2}-3a+2=0 \Rightarrow a=1, 2$. $a^{2}-5a+6=0 \Rightarrow a=2, 3$. $a^{2}-4=0 \Rightarrow a=\pm 2$. $a=2$ is the only solution.