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Solving Quadratic Inequality

CMAT 2023 · Quantitative Techniques & Data Interpretation · Easy · Algebra

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Find the range of values of real number x for which the inequality (x+2)(x+5)>40(x + 2)(x + 5) > 40 holds

  1. A.

    (−∞,−10)∪(3,∞)(-\infty, -10) \cup (3, \infty)

  2. B.

    (3,∞)(3, \infty)

  3. C.

    (−∞,1)∪(1,∞)(-\infty, 1) \cup (1, \infty)

  4. D.

    (−∞,10)(-\infty, 10)

Answer

A

Explanation

Expand the inequality: (x+2)(x+5)>40⇒x2+7x+10>40⇒x2+7x−30>0(x + 2)(x + 5) > 40 \Rightarrow x^2 + 7x + 10 > 40 \Rightarrow x^2 + 7x - 30 > 0 (x+10)(x−3)>0(x + 10)(x - 3) > 0

This holds for x<−10x < -10 or x>3x > 3. Thus, x∈(−∞,−10)∪(3,∞)x \in (-\infty, -10) \cup (3, \infty).

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