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
- A \((0,4)\)
- B \((-1,5)\)
- C \((-4,0)\)
- D \((-5,1)\)
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 \(D < 0 \Rightarrow(3-k)^2-16 < 0\)…
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