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TS EAMCET · Maths · Functions

For xR-{-6}, the value of (x+2)(x+5)(x+6) does not lie in the interval

  1. A [-9,-1]
  2. B [-5,-2]
  3. C (-5,-2)
  4. D (-9,-1)
Verified Solution

Answer & Solution

Correct Answer

(D) (-9,-1)

Step-by-step Solution

Detailed explanation

y=x+2x+5x+6 ⇒xy+6y=x2+7x+10 ⇒x2+7-yx+10-6y=0 For x to be real, ∆≥0 ⇒7-y2-410-6y≥0 y2-14y+49-40+24y≥0 ⇒y2+10y+9≥0 ⇒y+1y+9≥0 ⇒y∈(-∞,-9]∪[-1,∞)