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AP EAMCET · Maths · Functions

If \(\left|\frac{x^2+k x+1}{x^2+x+1}\right| < 3\) for all real numbers \(x\), then the range of the parameter \(k\) is

  1. A \((0,4)\)
  2. B \((-1,5)\)
  3. C \((-4,0)\)
  4. D \((-5,1)\)
Verified Solution

Answer & Solution

Correct Answer

(B) \((-1,5)\)

Step-by-step Solution

Detailed explanation

It is given, for all \(x \in R\) \(\begin{aligned} &\left|\frac{x^2+k x+1}{x^2+x+1}\right| 0, \forall x \in R\right] } \end{aligned}\) So, \(4 x^2+(k+3) x+4 > 0, \forall x \in R\) Then \(D 0, \forall x \in R\) Then \(D < 0 \Rightarrow(3-k)^2-16 < 0\)…