The number of distinct roots of the quadratic equation $a x^{2} + (a - 2) x + a^{2} - 4 = 0$ when $a = 2$ is

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Solution

For the equation $a x^{2} + (a - 2) x + a^{2} - 4 = 0$ when $a = 2$ , we can rewrite the equation as
$2 x^{2} = 0 \Rightarrow x = 0$
Hence the equation has only 1 distict root.

Also on comparing with the equation $p x^{2} + q x + r = 0$ , if $q = 0$ and $r = 0$ we know that the roots of the quadratic equation will be ${0, 0}$

Here, $a - 2 = 0$ and $a^{2} - 4 = 0$ . Hence we can directly say that the roots are ${0, 0}$ . Hence the equation has $1$ distinct root

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The number of distinct roots of the quadratic equation ax2+(a−2)x+a2−4=0 when a=2 is

The number of distinct roots of the quadratic equation $a x^{2} + (a - 2) x + a^{2} - 4 = 0$ when $a = 2$ is