AP and TS EAMCET Engineering Model Paper 8

y is real ⇒

(x+1)(x−3)

(x−2)

≥0
(x + 1)(x − 3) and (x − 2) have the same sign and (x − 2) ≠ 0
⇒ (x + 1)(x − 2) (x − 3) > 0, x ≠ 2
If x < − 1 then
x + 1 < 0, x − 2 < 0, x − 3 < 0 and Hence (x + 1) (x − 2) (x − 3) < 0
If −1< x < 2 then
x + 1 > 0, x − 2 < 0, x − 3 < 0 and Hence (x + 1) (x − 2) (x − 3) > 0
If 2 < x < 3 then
(x + 1) > 0, (x − 2) > 0, (x − 3) < 0 and Hence (x + 1) (x − 2) (x − 3) < 0
If x > 3 then
(x + 1) > 0, (x − 2) > 0, (x − 3) > 0 and Hence (x + 1) (x − 2) (x − 3) > 0
∴ −1 ≤ x < 2 or x ≥ 3