Mathematics 2011 JAMB Past Questions - Question 20: Solve the inequalities x² + 2x > 15

Correct Answer

D

Explanation

x² + 2x > 15 x² + 2x - 15 > 0x(x -3) + 5x – 15 > 0x(x-3) +5(x – 3) > 0(x -3 ) (x + 5) > 0 i.e x > 3 or x > -5 i.e -5 < x < 3 To solve the inequality x² + 2x > 15, we can start by rearranging the equation:x² + 2x - 15 > 0Next, we can factorize the quadratic expression:(x + 5)(x - 3) > 0Now, we can analyze the sign of the expression for different intervals:When x < -5:Both factors (x + 5) and (x - 3) are negative, so the product is positive. However, this interval is not part of the solution since it does not satisfy the inequality.When -5 < x < 3:The factor (x + 5) is positive, while the factor (x - 3) is negative. Therefore, the product is negative. This interval is part of the solution.When x > 3:Both factors (x + 5) and (x - 3) are positive, so the product is positive. This interval is also part of the solution.Therefore, the solution to the inequality x² + 2x > 15 is x < -5 or x > 3.