AP EAMCET · Maths · Quadratic Equation
If \(\left|\frac{x^2+k x+1}{x^2+x+1}\right| < 3\) for all real \(x\), then \(k\) is in the interval
- A \((-\infty,-1)\)
- B \((-1,6)\)
- C \((-1,5)\)
- D \((6, \infty)\)
Answer & Solution
Correct Answer
(C) \((-1,5)\)
Step-by-step Solution
Detailed explanation
\( -3 \( x^2+k x+1 0 \) \( D_1 = (3-k)^2 - 4(2)(2) \( x^2+k x+1 > -3(x^2+x+1) \Rightarrow 4x^2+(k+3)x+4 > 0 \) \( D_2 = (k+3)^2 - 4(4)(4) \( k \in (-1, 7) \cap (-11, 5) \Rightarrow k \in (-1, 5) \)
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