Homework: Quadratic Equations and Inequalities
Part A: Solve the following quadratic equations
1.
2.
3.
4.
5.
x² − 5x + 6 = 0
2x² + 7x + 3 = 0
3x² − 12 = 0
x² + 4x − 21 = 0
4x² − 20x + 25 = 0
Part B: Solve the following quadratic inequalities
6. x² − 9 > 0
7. x² − 5x + 6 ≤ 0
8. 2x² + x − 3 > 0
9. x² + 4x + 3 < 0
10. 3x² − 12x + 9 ≥ 0
Part C: Problems
3. The product of two consecutive integers is 72. Find the two integers.
4. A rectangular garden is enclosed by 40 metres of fencing. The length of the garden is x metres.
(a) Show that the area A of the garden can be written as: A=x(20−x)
(b) Write down an inequality for the values of x that give an area of at least 96 m².
(c) Solve the inequality and state the range of possible lengths for the garden.
Good luck! Show all your steps clearly.