Solve -x2 + 3x – 2 ≥ 0 – InterviewSolution

1.	Solve -x2 + 3x – 2 ≥ 0
Answer» -x² + 3x – 2 ≥ 0 ⇒ x² – 3x + 2 ≤ 0 (x – 1) (x – 2) ≤ 0 [(x – 1) (x – 2) = 0 ⇒ x = 1 or 2. Here α = 1 and β = 2. Note that α < β] So for the inequality (x – 1) (x – 2) ≤ 2 x lies between 1 and 2 (i.e.) x ≥ 1 and x ≤ 2 or x ∈ [1, 2] or 1 ≤ x ≤ 2

Solve -x2 + 3x – 2 ≥ 0

Answer»

-x² + 3x – 2 ≥ 0 ⇒ x² – 3x + 2 ≤ 0

(x – 1) (x – 2) ≤ 0

[(x – 1) (x – 2) = 0 ⇒ x = 1 or 2. Here α = 1 and β = 2. Note that α < β]

So for the inequality (x – 1) (x – 2) ≤ 2

x lies between 1 and 2

(i.e.) x ≥ 1 and x ≤ 2 or x ∈ [1, 2] or 1 ≤ x ≤ 2