Cambridge Additional Mathematics

Quadratics (Chapter 3) 71

For example, consider the Acme Leather Jacket Co. equation from page 65.

We need to solve: 12 : 5 x^2 ¡ 550 x+ 5125 = 0

so in this case a=12: 5 , b=¡ 550 , c= 5125

) x=

550 §

p

(¡550)^2 ¡4(12:5)(5125)

2(12:5)

=

550 §

p

46 250

25

¼ 30 : 60 or 13 : 40

However, for this application the number of jacketsxneeds to be a whole

number, so x=13or 31 would produce a profit of around $ 3000 each

week.

Example 7 Self Tutor

Solve forx:

a x^2 ¡ 2 x¡6=0 b 2 x^2 +3x¡6=0

b 2 x^2 +3x¡6=0has

a=2, b=3, c=¡ 6

) x=

¡ 3 §

p

32 ¡4(2)(¡6)

2(2)

) x=

¡ 3 §

p

9+48

4

) x=

¡ 3 §

p

57

4

EXERCISE 3A.3

1 Use the quadratic formula to solve exactly forx:

a x^2 ¡ 4 x¡3=0 b x^2 +6x+7=0 c x^2 +1=4x

d x^2 +4x=1 e x^2 ¡ 4 x+2=0 f 2 x^2 ¡ 2 x¡3=0

g 3 x^2 ¡ 5 x¡1=0 h ¡x^2 +4x+6=0 i ¡ 2 x^2 +7x¡2=0

2 Rearrange the following equations so they are written in the form ax^2 +bx+c=0, then use the

quadratic formula to solve exactly forx.

a (x+ 2)(x¡1) = 2¡ 3 x b (2x+1)^2 =3¡x c (x¡2)^2 =1+x

d (3x+1)^2 =¡ 2 x e (x+ 3)(2x+1)=9 f (2x+ 3)(2x¡3) =x

g

x¡ 1

2 ¡x

=2x+1 h x¡

1

x

=1 i 2 x¡

1

x

=3

Trying to factorise this

equation or using

‘completing the square’

would not be easy.

a x^2 ¡ 2 x¡6=0has

a=1, b=¡ 2 , c=¡ 6

) x=

¡(¡2)§

p

(¡2)^2 ¡4(1)(¡6)

2(1)

) x=

2 §

p

4+24

2

) x=

2 §

p

28

2

) x=

2 § 2

p

7

2

) x=1§

p

7

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_03\071CamAdd_03.cdr Friday, 17 January 2014 3:57:23 PM BRIAN