Quadratic Inequality

CAT 1996 Slot 1 · QA · Easy · QA

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Which of the following values of xx do not satisfy the inequality (x2−3x+2>0)(x^2 - 3x + 2 > 0) at all?

  1. A.

    1≤x≤21 \le x \le 2

  2. B.

    −1≥x≥−2-1 \ge x \ge -2

  3. C.

    0≤x≤20 \le x \le 2

  4. D.

    0≥x≥−20 \ge x \ge -2

Answer

A

Explanation

(x−1)(x−2)>0  ⟹  x>2(x-1)(x-2) > 0 \implies x > 2 or x<1x < 1. Thus no value in 1≤x≤21 \le x \le 2 satisfies the inequality.

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