99 Percentile Qs Bank for JEE MainMathematicsBasics of Mathematics
Set of all the values of x satisfying the inequality x 2 - 7 x + 6 > x + 2 is
Options
- Ax ∈ - ∞ , 2 11
- Bx ∈ 2 11 , ∞
- Cx ∈ - ∞ , 1 ∪ 6 , ∞
- Dx ∈ 6 , ∞
Correct answer
A. x ∈ - ∞ , 2 11
Step-by-step solution
x 2 - 7 x + 6 ≥ 0 ⇒ x ∈ - ∞ , 1 ∪ 6 , ∞ Case I: x < - 2 LHS is non negative, RHS is negative ⇒ the inequality is always true ⇒ x < - 2 . Case II: x ≥ - 2 x 2 - 7 x + 6 > x 2 + 4 x + 4 - 11 x > - 2 ⇒ x < 2 11 ⇒ x ∈ - 2 , 2 11 Taking the union of the two cases, we get, x ∈ - ∞ , 2 11