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If - 3 < x 2 - λ x - 2 x 2 + x + 1 < 2 for all x ∈ R , then the value of λ belongs to

Options

  1. A- 1,7
  2. B- 6,2
  3. C- 1,2
  4. D- 6,7

Correct answer

C. - 1,2

Step-by-step solution

- 3 &#60; x 2 - &#955; x - 2 x 2 + x + 1 &#60; 2 &#8658; - 3 x 2 - 3 x - 3 &#60; x 2 - &#955; x - 2 &#60; 2 x 2 + 2 x + 2 since &#160; x 2 + x + 1 &#62; 0 , &#160; &#8704; x &#8712; R &#8658; 4 x 2 + x 3 - &#955; + 1 &#62; 0 , x 2 + x 2 + &#955; + 4 &#62; 0 i &#160; 4 x 2 - x &#955; - 3 + 1 &#62; 0 &#8658; D &#60; 0 &#8658; &#955; - 3 2 - 4 &#215; 4 &#215; 1 &#60; 0 &#8658; &#955; - 3 + 4 &#955; - 3 - 4 &#60; 0 &#8658; &#955; + 1 &#955; - 7 &#60; 0 &#8658; &#955; &#8712; - 1,7 i i &#160; x 2 + x &#955; + 2 + 4 &#62

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