Mathematics 2008 JAMB Past Questions - Question 18: Solve the quadratic inequality x2 -5x+6>0

Correct Answer

A

Explanation

xsup2 - 5x +6 >0xsup2 - 2x - 3x +6 >0x (x-2) -3x (x-2) > 0(x-2) (x-3) > 0x>2 or x > 3x < 2 > 3To solve the quadratic inequality \(x^2 - 5x + 6 > 0\), we can first find the roots of the corresponding quadratic equation \(x^2 - 5x + 6 = 0\), and then use the roots to determine the intervals where the inequality is satisfied.To find the roots, we can factorize the quadratic equation:\(x^2 - 5x + 6 = (x - 2)(x - 3) = 0\)So the roots are \(x = 2\) and \(x = 3\).Now, we can use these roots to determine the intervals where the inequality is satisfied. We can do this by plotting the roots on a number line and testing the inequality in the intervals between the roots.We have three intervals to test: \((-\infty, 2)\), \((2, 3)\), and \((3, \infty)\).Testing the inequality in the interval \((-\infty, 2)\):Choose \(x = 0\), then \(0^2 - 5(0) + 6 = 6 > 0\), so this interval satisfies the inequality.Testing the inequality in the interval \((2, 3)\):Choose \(x = 2.5\), then \(2.5^2 - 5(2.5) + 6 = 6.25 - 12.5 + 6 = 0.75 > 0\), so this interval satisfies the inequality.Testing the inequality in the interval \((3, \infty)\):Choose \(x = 4\), then \(4^2 - 5(4) + 6 = 16 - 20 + 6 = 2 < 0\), so this interval does not satisfy the inequality.Therefore, the solution to the inequality \(x^2 - 5x + 6 > 0\) is \(x \in (-\infty, 2) \cup (2, 3)\).