J17

x = 3
1
or x = 7
Exercise : Solve.
1. (x + 4)(x + 2) = 0 2. (x – 5)(x – 3) = 0
3. (x – 5)(x + 7) = 0 4. (x – 9) 2 = 0
5. (x + 13) 2 = 0 6. x 2 + x – 12 = 0
7. x 2 + 9x + 14 = 0 8. x 2 – 11x – 12 = 0
9. u 2 + 6u + 9 = 0 10. t 2 – t – 42 = 0
11. a 2 – 2a + 1 = 0 12. y 2 + 8y = 0
13. x 2 + 10x = 24 14. x 2 = 4x – 3
15. v 2 – 36 = 0 16. 4x 2 – 9 = 0
17. 1 – y 2 = 0 18. 81 – 16q 2 = 0
19. x 2 = 6x 20. 5x 2 = 45
21. 6x(2x + 3) = 0 22. -4x(3x – 5) = 0
23. (3x – 2)(2x + 1) = 0 24. 6x 2 – 29x + 35 = 0
25. 6x 2 – x + 1 = 0 26. (4x – 3)(3x – 4) = 0
27. 4y 2 – 48y = 16 28. 3y 2 – 24y = 3
Solutions of quadratic equations by formula
The solutions of the quadratic equation ax 2 + bx + c = 0 are given by the formula
b
( b
2 4ac)
x
2a
Use this formula only after trying (and failing) to factorise.
Example
Solve the equation 2x 2 – 3x – 4 = 0.
Solution
In this case a = 2, b = -3, c = -4.
2
( 3)
( 3)
(4
2 4)
x =
=
2
2
3 9
32
3 ± 41 3 ± 6.403
=
= =
4
4 4
3 + 6.403
3
6.403
Either x = = 2.35 ( 2 d.p ) or -0.85 (2 d.p)
4
3