InterviewSolution
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InterviewSolution
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(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 intervalA. `(- oo, 3]`B. `(-oo, -2) uu (2, oo)`C. `[-2, 2]`D. `[-3, oo)` |
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Answer» Correct Answer - 2 `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`. |
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