Solve the inequality (x^{2} – 2x geq 3)
-
A.
(-1 leq x leq 3) -
B.
(x geq 3) and (x leq -1) -
C.
(x geq 3) or (x -
D.
(-1 leq x
Correct Answer: Option B
Explanation
(x^{2} – 2x geq 3 implies x^{2} – 2x – 3 geq 0)
(x^{2} + x – 3x – 3 = (x + 1)(x – 3) geq 0)
(x = -1 ; x = 3)
Check: (x = -1 : (-1)^{2} – 2(-1) = 1 + 2 geq 3) (satisfied)
(-1 < x < 3 : 0^{2} – 2(0) = 0 geq 3) (not satisfied)
(x < -1 : (-2)^{2} – 2(-2) = 4 + 4 = 8 geq 3) (satisfied)
(x = 3 : 3^{2} – 2(3) = 9 – 6 = 3 geq 3) (satisfied)
(x > 3 : 4^{2} – 2(4) = 16 – 8 = 8 geq 3) (satisfied)
(therefore x^{2} – 2x geq text{3 is satisfied in the region x} leq text{-1 and x} geq 3)