(B) (2, 9/4) If two roots of the equation `(a-1) (x^2 + x + 1 )^2-(a + 1) (x^4 + x^2 + 1) = 0` are real and distinct, then a lies in the interval

Options

A. `(- oo, 3]`
B. `(-oo, -2) uu (2, oo)`
C. `[-2, 2]`
D. `[-3, oo)`

Answer

2

Explanation

`x^(4) + x^(2) + 1 = (x^(2) + 1)^(2) - x^(2)`
`= (x^(2) + x + 1)(x^(2) - x + 1)`
`x^(2) + x + 1 = (x + 1/2)^(2) + 3/4 ne 0 AA x`
Therefore, we can cancel this factor and we get
`(a - 1)(x^(2) - x + 1) = (a + 1)(x^(2) - x + 1)`
or `x^(2) - ax + 1 = 0`
It has real and distinct roots if `D = a^(2) - 4 gt 0`.