Question

If equation $(a-2)x^2+(a^2-4a+4)x+(a^2–4)=0$ has more than two roots then $a$ is

Answer 1

$(a-2)x^2+(a^2-4a+4)x+(a^2–4)=0$

$(a-2)x^2+(a^2-2a-2a+4)x+(a-2)(a+2)=0$

$\Rightarrow (a-2)x^2+(a-2)(a-2)x+(a-2)(a+2)=0$ as it is an identity.

$\Rightarrow a-2=0\Rightarrow a=2$

$\Rightarrow (a-2)(a-2)=0\Rightarrow a=2,2$

$\Rightarrow (a-2)(a+2)=0\Rightarrow a=-2,2$

So,$\left\{2\right\}\cap \left\{2\right\}\cap \{-2,2\}=2$

So $a=2$