To solve the inequalities, we can first find the roots of each quadratic equation.
1) For the inequality x² - 3x + 2 > 0:
To find the roots of x² - 3x + 2 = 0, we can factorize the quadratic equation(x - 1)(x - 2) = This gives us roots x = 1 and x = 2.
The inequality x² - 3x + 2 > 0 means the quadratic is greater than zero when x is between the roots, so the solution is1 < x < 2
2) For the inequality x² + 5x + 6 ≤ 0:
To find the roots of x² + 5x + 6 = 0, we can factorize the quadratic equation(x + 2)(x + 3) = This gives us roots x = -2 and x = -3.
The inequality x² + 5x + 6 ≤ 0 means the quadratic is less than or equal to zero when x is between the roots, so the solution is-3 ≤ x ≤ -2
Therefore, the solutions to the inequalities are1 < x < 2 and -3 ≤ x ≤ -2
To solve the inequalities, we can first find the roots of each quadratic equation.
1) For the inequality x² - 3x + 2 > 0:
To find the roots of x² - 3x + 2 = 0, we can factorize the quadratic equation
(x - 1)(x - 2) =
This gives us roots x = 1 and x = 2.
The inequality x² - 3x + 2 > 0 means the quadratic is greater than zero when x is between the roots, so the solution is
1 < x < 2
2) For the inequality x² + 5x + 6 ≤ 0:
To find the roots of x² + 5x + 6 = 0, we can factorize the quadratic equation
(x + 2)(x + 3) =
This gives us roots x = -2 and x = -3.
The inequality x² + 5x + 6 ≤ 0 means the quadratic is less than or equal to zero when x is between the roots, so the solution is
-3 ≤ x ≤ -2
Therefore, the solutions to the inequalities are
1 < x < 2 and -3 ≤ x ≤ -2