InterviewSolution
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InterviewSolution
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Find the values of `k`for which`|(x^2+k x+1)/(x^2+x+1)| |
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Answer» We have `|x| lt a `rArr - a lt x lt + a` Therefore, the given inequality implies `-2lt(x^(2) + kx + 1)/(x^(2) + x + 1) lt 2` (2) Now, `x^(2) + x +1 = (x+ 1//x)^(2) + (3//4)` is positive for all values of x. Multiplying (1) by `x^(2) + x + 1,` we get ` -2(x^(2) + x+1) lt x^(2) + kx + 1 lt 2(x^(2) + x + 1)` This yields two inequalities, viz., `3x^(2) + (2+k)x + 3) gt`0 and `x^(2) + (2-k) x + 1 lt 0` For above inequalities to be. ture for all values of x, their discrimainats must be negative . Hence, `(2+k)^(2) - 36 lt 0 and (2 - k)^(2) - 4 lt 0` (2) `rArr (k+ 8) (k - 4) lt 0 and k (k - 4) lt 0` (3) `rArr - 8 lt k lt 4 and 0 lt k lt 4` Therefore, `0lt k lt 4` |
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