Everything Maths Grade 11

7.4 CHAPTER 7. SOLVINGQUADRATIC EQUATIONS

8. 9 t^2 − 7 t− 9 = 0


9. 2 t^2 + 3t + 2 = 0


10. t^2 + t + 1 = 0

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(1.) 0190 (2.) 0191 (3.) 0192 (4.) 0193 (5.) 0194 (6.) 0195

(7.) 0196 (8.) 0197 (9.) 0198 (10.) 0199

Tip

• In all the ex-
  amples done so
  far, the solutions
  were left in surd
  form. Answers
  can also be
  given in decimal
  form, using the
  calculator. Read
  the instructions
  when answering
  questions in a test
  or exam whether
  to leave answers
  in surd form, or
  in decimal form
  to an appropri-
  ate number of
  decimal places.


• Completing
  the square as a
  method to solve
  a quadratic equa-
  tion is only done
  when specifically
  asked.

Exercise 7 - 4

Solve the quadratic equations by either factorisation, completing the square or by using the quadratic

formula:

• Always try to factorisefirst, then use the formula if the trinomial cannot be factorised.


• Do some of them by completing the square and then compare answers to those done using the
  other methods.

1. 24 y^2 + 61y− 8 = 0

2 .− 8 y^2 − 16 y + 42 = 0

3 .− 9 y^2 + 24y− 12 = 0

4 .− 5 y^2 + 0y + 5 = 0

5 .− 3 y^2 + 15y− 12 = 0

6. 49 y^2 + 0y− 25 = 0

7 .− 12 y^2 + 66y− 72 = 0

8 .− 40 y^2 + 58y− 12 = 0

9 .− 24 y^2 + 37y + 72 = 0

10. 6 y^2 + 7y− 24 = 0

11. 2 y^2 − 5 y− 3 = 0

12 .− 18 y^2 − 55 y− 25 = 0

13 .− 25 y^2 + 25y− 4 = 0

14 .− 32 y^2 + 24y + 8 = 0

15. 9 y^2 − 13 y− 10 = 0

16. 35 y^2 − 8 y− 3 = 0

17 .− 81 y^2 − 99 y− 18 = 0

18. 14 y^2 − 81 y + 81 = 0

19 .− 4 y^2 − 41 y− 45 = 0

20. 16 y^2 + 20y− 36 = 0

21. 42 y^2 + 104y + 64 = 0

22. 9 y^2 − 76 y + 32 = 0

23 .− 54 y^2 + 21y + 3 = 0

24. 36 y^2 + 44y + 8 = 0

25. 64 y^2 + 96y + 36 = 0

26. 12 y^2 − 22 y− 14 = 0

27. 16 y^2 + 0y− 81 = 0

28. 3 y^2 + 10y− 48 = 0

29 .− 4 y^2 + 8y− 3 = 0

30 .− 5 y^2 − 26 y + 63 = 0

31. x^2 − 70 = 11

32. 2 x^2 − 30 = 2

33. x^2 − 16 = 2− x^2

34. 2 y^2 − 98 = 0

35. 5 y^2 − 10 = 115

36. 5 y^2 − 5 = 19− y^2

More practice video solutions or help at http://www.everythingmaths.co.za

(1.) 01zs (2.) 01zt (3.) 01zu (4.) 01zv (5.) 01zw (6.) 01zx

(7.) 01zy (8.) 01zz (9.) 0200 (10.) 0201 (11.) 0202 (12.) 0203

(13.) 0204 (14.) 0205 (15.) 0206 (16.) 0207 (17.) 0208 (18.) 0209

(19.) 020a (20.) 020b (21.) 020c (22.) 020d (23.) 020e (24.) 020f

(25.) 020g (26.) 020h (27.) 020i (28.) 020j (29.) 020k (30.) 020m

(31.) 020n (32.) 020p (33.) 020q (34.) 020r (35.) 020s (36.) 020t