The number of values of $a$ for which $(a^{2} - 3 a + 2) x^{2} + (a^{2} - 5 a + 6) x + a^{2} - 4 = 0$ is an identity in $x$ is-

0

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Solution

The correct option is C $1$
Equation is a identity if all its coefficients are equal to zero simultaneously

$\Rightarrow a^{2} - 3 a + 2 = 0$

$\Rightarrow a = 2, 1$

$\Rightarrow a^{2} - 5 a + 6 = 0$

$\Rightarrow a^{2} - 4 = 0$

$\Rightarrow a = \pm 2$

$\Rightarrow$ coefficients are equal to zero simultaneously when $a = 2$

Therefore only one value of 'a' the equation is identity in $x$

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