Find the solutions for the following quadratic equations by factorising when needed.
1. (x + 2)(x − 5) = 0 |
9. a2 − 121 = 0 |
2. (x − 9)(x + 9) = 0 |
10. |
3. (s − 4)(s − 8) = 0 |
11. x2 − x = 12 |
4. p2 + 15p − 16 = 0 |
12. (y − 5)2 = 0 |
5. r2 + r − 12 = 0 |
13. (2r + 5)(3r − 2) = 0 |
6. 3y(4y − 5) = 0 |
14. (4s − 3)(5s − 1) = 0 |
7. x(x − 8) = 0 |
15. 3t2 + 2t − 1 = 0 |
8. (x − 9)2 − 9 = 0 |
16. (x + 5)2 = 25 |
Find the solutions for the following quadratic equations, to 2 decimal places, by using the quadratic formula:
17. p2 + 8p +3 = 0 | 20. 0.8x2 + 1.6x + 0.2 = 0 |
18. s2 − 7s + 4 = 0 |
21. (2x − 3)2 = 8 |
19. 3y2 + 6y − 7 = 0 | 22. x + √x = 1 |
Find the solutions for the following quadratic equations:
23. (b + 7)2 = 0 | 28. 3y(y − 6) = 0 |
24. x2 − 6x + 4 = 0 |
29. t 2 − 7t + 6 = 0 |
25. 2(d + 4)(d − 4) = 0 | 30. 8q2 + q − 12 = 0 |
26. (y − 9)(3y + 2) = 0 | 31. x2 = 8x + 20 |
27. 2x2 − 7x + 1 = 0 |
32. 2r2 + 3r = 1 + r2 |
For questions 33 to 40 make up a quadratic equation to help solve the problems.
33. A farmer's rectangular paddock is 20m longer than it is wide. Its area is 2400 m2. Find its length and width.
34. The width of a rectangular car park is 10 m less than its length. The area of the car park is 7200 m2. Find the length and width of the car park.
35. A box is 12 cm high. Its volume is 1800 cm3. Its length is 5 cm more than its width. Find its length and width.
36. Janice and Edita ages are different by 5 years. Edita is the youngest. The product of their ages is 864. How old is Janice?
37. The base of a right-angled triangle is one metre more than the height of the triangle. The length of the hypotenuse is 6 metres. Find the lengths of the height and base.
38. The product of two consecutive odd numbers is 2115. What are the two numbers?
39. The sides of a rectangle are (x + 3) cm and (x + 5) cm. If the area of the rectangle is 25 cm2, find the lengths of the sides.
40. The three sides of a right-angled triangle are x cm, (x + 1) cm and (x + 4) cm.
Find the value of x correct to 3 significant figures.