The value of $a$ for which the equation $(a^{2} - a - 2) x^{2} + (a^{2} - 4) x + (a^{2} - 3 a + 2) = 0$ have more than two roots

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Solution

The correct option is C $2$
Since, the given equation have more than two roots so this is identity.

Thus given equation is satisfied for all values of $x$ , so all the coeffients must be zero. Then,
$a^{2} - a - 2 = 0 \Rightarrow a = - 1, 2$
$a^{2} - 4 = 0 \Rightarrow a = - 2, 2$
$a^{2} - 3 a + 2 = 0 \Rightarrow a = 1, 2$
Therefore, the common value of $a = 2$

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