Question

Number of values of a for which the equation ( $a^2$ - 5a + 4) $x^2$ + ( $a^2$ - 1) x + ( $a^2$ - 8a + 7) = 0 possesses more than two roots, is__.

Answer 1

If a quadratic equation has more than two roots, it is an identity.

For the given equation to be an identity, all the three coefficients should be zero.

$a^2$ - 5a + 4 = 0, $a^2$ - 1 = 0, $a^2$ - 8a + 7 = 0

a = 1 or 4, a = 1 or - 1, a = 7 or 1

All the three will be zero when a = 1 or 1 is a common root.

⇒ Only at one value of a the given equation can be considered as an identity.