Cambridge International Mathematics

Example 27 Self Tutor

The sum of a number and its square is 42. Find the number.

Let the number bex. Therefore its square isx^2.

x+x^2 =42

) x^2 +x¡42 = 0 frearrangingg

) (x+ 7)(x¡6) = 0 ffactorisingg

) x=¡ 7 or x=6

So, the number is¡ 7 or 6. Check: Ifx=¡ 7 , ¡7+(¡7)^2 =¡7 + 49 = 42 X

Ifx=6, 6+6^2 =6+36=42X

Example 28 Self Tutor

A rectangle has length 5 cm greater than its width. If it has an area of 80 cm^2 , find the

dimensions of the rectangle, to the nearest mm.

Ifxcm is the width, then(x+5)cm is the length.

Now area=80cm^2

) x(x+5)=80

) x^2 +5x=80

) x^2 +5x¡80 = 0

Using a graphics calculator, the graph of

y=x^2 +5x¡ 80 is:

Example 29 Self Tutor

Given that BC is 3 m longer than AB,

find the height of the flag pole.

Let the height of the pole bexm.

) BC=xm and AB=(x¡3)m

The triangles are equiangular, so they are similar.

Hence

2

x¡ 3

=

x

(x¡3) +x

AB C

2m

2m

xm

xm

a

a

()x¡-¡3 m

(5)cmx¡+¡

xcm

Asxis clearly positive,

x¼ 6 : 8 cm (to the nearest mm).

) the rectangle is approx. 11 : 8 cm by 6 : 8 cm.

448 Quadratic equations and functions (Chapter 21)

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Y:\HAESE\IGCSE01\IG01_21\448IGCSE01_21.CDR Monday, 10 November 2008 12:40:43 PM PETER