NTA Abhyas JEE Main2020MathematicsFunctionsPractice

For real values of x , the value of the expression 11 x 2 - 12 x - 6 x 2 + 4 x + 2

Options

Alies between - 17 and - 3
Bdoes not lie between - 17 and - 3
Clies between 3 and 17
Ddoes not lie between 3 and 17

Correct answer

B. does not lie between - 17 and - 3

Step-by-step solution

Let y = 11 x 2 - 12 x - 6 x 2 + 4 x + 2 y x 2 + 4 y x + 2 y = 11 x 2 - 12 x - 6 y - 11 x 2 + 4 y + 12 x + 2 y + 6 = 0 x ∈ R ⇒ D ≥ 0 ⇒ 4 y + 3 2 - 4 y - 11 2 y + 3 ≥ 0 ⇒ 8 y + 3 2 y + 3 - y - 11 ≥ 0 ⇒ 8 y + 3 y + 17 ≥ 0 ⇒ y ≤ - 17 or y ≥ - 3 ⇒ y does not lie between - 17 and - 3

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