Cambridge Additional Mathematics

(x + ) 3 cm

xcm

f(x)

O x

f(x) = 2x 2 -x-2

P,(0 3)

Quadratics (Chapter 3) 93

8 Show that any linear function passing through P(0,3)

will meet the curve f(x)=2x^2 ¡x¡ 2 twice.

Some real world problems can be solved using a quadratic equation. We are generally only interested in any

real solutionswhich result.

Any answer we obtain must be checked to see if it is reasonable. For example:

² if we are finding a length then it must be positive and we reject any negative solutions

² if we are finding ‘how many people are present’ then clearly the answer must be a positive integer.

We employ the following general problem solving method:

Step 1: If the information is given in words, translate it into algebra using a variable such asxfor the

unknown. Write down the resulting equation. Be sure to define what the variablexrepresents,

and include units if appropriate.

Step 2: Solve the equation by a suitable method.

Step 3: Examine the solutions carefully to see if they are acceptable.

Step 4: Give your answer in a sentence.

Example 26 Self Tutor

A rectangle has length 3 cm longer than its width. Its area is 42 cm^2. Find its width.

If the width isxcm then the length is (x+3)cm.

) x(x+3)=42 fequating areasg

) x^2 +3x¡42 = 0

) x=

¡ 3 §

p

32 ¡4(1)(¡42)

2

) x=

¡ 3 §

p

177

2

) x¼¡ 8 : 15 or 5 : 15

We reject the negative solution as lengths are positive.

The width is about 5 : 15 cm.

EXERCISE 3G

1 Two integers differ by 12 and the sum of their squares is 74. Find the integers.

2 The sum of a number and its reciprocal is^265. Find the number.

G Problem solving with quadratics

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_03\093CamAdd_03.cdr Thursday, 3 April 2014 5:00:46 PM BRIAN