If the two roots of the equation, a - 1 x 4 + x 2 + 1 + a + 1 x 2 + x + 1 2 = 0 are real and distinct, then the set of all values of a is equal to

Step-by-step solution

a - 1 x 4 + x 2 + 1 + a + 1 x 2 + x + 1 2 = 0 x 2 + x + 1   a - 1 x 2 - x + 1 + a + 1 ( x 2 +   x + 1 ) = 0 x 2 + x + 1 2 a x 2 + 2 x + 2 a = 0 ⇒  x 2 + x + 1   a x 2 + x + a = 0 If two Roots are real Then, roots of a x 2 + x + a = 0 should be real & distinct. ∴ 1 - 4 a 2 > 0 1 - 2 a 1 + 2 a > 0 As a ≠ 0 therefore a ∈ - 1 2 , 0   ∪ 0 , 1 2