For the equation ax2+(a−2)x+a2−4=0 when a=2, we can rewrite the equation as
2x2=0⇒x=0
Hence the equation has only 1 distict root.
Also on comparing with the equation px2+qx+r=0, if q=0 and r=0 we know that the roots of the quadratic equation will be {0,0}
Here, a−2=0 and a2−4=0. Hence we can directly say that the roots are {0,0}. Hence the equation has 1 distinct root