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Quadratic Inequality Solution

CMAT 2018 · Quantitative Techniques & Data Interpretation · Easy · Algebra

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If y2+3y−18≥0y^2 + 3y - 18 \ge 0, which of the following is true?

  1. A.

    y≤3 or y≥0y \le 3 \text{ or } y \ge 0

  2. B.

    y>−6 or y<3y > -6 \text{ or } y < 3

  3. C.

    −6≤y≤3-6 \le y \le 3

  4. D.

    y≥3 or y≤−6y \ge 3 \text{ or } y \le -6

Answer

D

Explanation

Factorize the quadratic expression: y2+3y−18=(y+6)(y−3)≥0y^2 + 3y - 18 = (y + 6)(y - 3) \ge 0. Critical points are y=−6y = -6 and y=3y = 3. For the product to be ≥0\ge 0, y≥3y \ge 3 or y≤−6y \le -6.

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