WORKED SOLUTIONS

2
Answers
Skills check
1 a

Quadratic functions and equations d x 2 − 25 = 0 (x + 5) (x − 5) = 0 x = ±5

3a − 5 = a + 7 2a = 12 a=6 4 x 2 + 1 = 21 4x 2 = 20 x2 = 5 x =± 5 3(n − 4) = 5(n + 2) 3n − 12 = 5n + 10 2n = −22 n = −11 2k(k − 5) 7a(2a2 + 3a − 7) 2 x 2 + 4 xy + 3 x + 6 y 2x ( x + 2 y ) + 3( x + 2 y )
2

e

x 2 + 2x − 48 = 0 x2 + 8x − 6x − 48 = 0

x(x + 8) − 6(x + 8) = 0 (x + 8) (x − 6) = 0 x = −8 or x = 6 f b

b 2 + 6b + 9 = 0 b 2 + 3b + 3b + 9 = 0 b(b + 3) + 3(b + 3) = 0 (b + 3)2 = 0 b = −3

c

2

a b c

a

6x 2 + 5x − 4 = 0 6x 2 + 8x − 3x − 4 = 0 2x(3x + 4) − 1(3x + 4) = 0 (3x + 4)(2x − 1) = 0 x = − 3 or x =
4 1 2

( 2x + 3) ( x + 2 y )

5a 2 − 10a − ab + 2b 5a ( a − 2 ) − b ( a − 2 ) ( 5a − b ) ( a − 2 ) e (n + 1)(n + 3) f (2x − 3)(x + 1) g (m + 6)(m − 6) h (5x + 9y)( 5x − 9y) d b

5c 2 + 6c − 8 = 0 5c 2 + 10c − 4c – 8 = 0 5c (c + 2) − 4 (c + 2) = 0 (c + 2) (5c − 4) = 0 c = −2 or c = 5
4

Exercise 2A
1 a

c

b

c

x 2 − 3x + 2 = 0 x 2 − x − 2x + 2 = 0 x(x − 1) − 2(x − 1) = 0 (x − 1)(x − 2) = 0 x = 1 or x = 2 a 2 + a − 56 = 0 a 2 + 8a − 7a − 56 = 0 a(a + 8) − 7(a + 8) = 0 (a + 8)(a − 7) = 0 a = −8 or a = 7 m 2 − 11m + 30 = 0 m 2 − 5m − 6m + 30 = 0 m(m − 5) − 6(m − 5) = 0 (m − 5) (m − 6) = 0 m = 5 or m = 6

2h 2 − 3h − 5 = 0 2h 2 − 5h + 2h − 5 = 0 h(2h − 5) + 1(2h − 5) = 0 (h + 1) (2h − 5) = 0 h = −1 or h = 2
5

d

4x 2 − 16x − 9 = 0 4x 2 − 18x + 2x – 9 = 0 2x(2x – 9) + 1(2x – 9) = 0 (2x + 1) (2x − 9) = 0 x = − 1 or x =
2 9 2

e

3t 2 + 14t + 8 = 0 3t 2 + 12t + 2t + 8 = 0 3t (t + 4) + 2(t + 4) = 0 (t + 4) (3t + 2) = 0 t = −4 or t = − 3
2

© Oxford University Press 2012: this may be reproduced for class use solely for the purchaser’s institute

Worked solutions: Chapter 2

1

WORKED SOLUTIONS f 6x 2 + x − 12 = 0 6x 2 + 9x − 8x − 12 = 0 3x(2x + 3) − 2(2x +