The number of value(s) of $a$ for which the equation $(a^{2} + 2 a + 1) x^{3} + (a - 1) x^{2} - (a + 1) x = 0$ is an identity is

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

000

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

0.0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

Given: $(a^{2} + 2 a + 1) x^{3} + (a - 1) x^{2} - (a + 1) x = 0$ is an identity.
Thus, the coefficients of $x$ are all equal to $0$
$\Rightarrow a^{2} + 2 a + 1 = 0 \Rightarrow (a + 1)^{2} = 0 \Rightarrow a = - 1 \dots (1)$
Similarly, $a - 1 = 0 \Rightarrow a = 1 \dots (2)$
And $a + 1 = 0 \Rightarrow a = - 1 \dots (3)$
Thus, from all these equations, we get no unique value of $a .$
Thus, the number of values of $a$ for which the equation is an identity is $0$

Suggest Corrections

Similar questions

(a^{2} - 1) x^{2} + (a - 1) x + a^{2} - 4 a + 3 = 0

x

The values of a for which( $a^{2} - 1$ ) $x^{2}$ + 2(a-1)x + 2 is positive for any x are

The values of ‘a’ for which $(a^{2} - 1) x^{2} + 2 (a - 1) x + 2$ is positive for any $x$ are

The values of 'a' for which( a²-1)x²+2(a-1)x+2 is positive for all real x are

(a - 1) x^{2} + (a^{2} - 2 a + 1) x + (a^{2} - 1) = 0

a

Join BYJU'S Learning Program