Find the range of values of x for which x² + 4x + 5 is less than 3x² - x + 2

Correct Answer is : x<−12, x>3x < -1/2,\; x > 3x<2−1,x>3

Correct Answer is : x<−12, x>3x < -1/2,\; x > 3x<2−1,x>3

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WAEC Further Mathematics 2013 Paper

Question : 13

Total: 40

x^{2} + 4x + 5

3x^{2} - x + 2

Solution:

Concept:

Rearrange the quadratic inequality to one side, factor it, and determine the sign intervals.

Explanation:

Start with

x^2 + 4x + 5 < 3x^2 - x + 2

Bring all terms to one side:

0 < 2x^2 - 5x - 3

Factor the quadratic expression:

2x^2 - 5x - 3 = (2x + 1)(x - 3)

So we need

(2x + 1)(x - 3) > 0

The critical points are

x = -\frac{1}{2}

and

x = 3

The product is positive only when

x

lies outside these roots.

Therefore, the inequality holds for

x < -\frac{1}{2}

x > 3

Answer:

x < -\frac{1}{2}

x > 3

, which is option B.

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