) 2(2x¡3) =x(x¡3)
) 4 x¡6=x^2 ¡ 3 x
) 0=x^2 ¡ 7 x+6
) (x¡1)(x¡6) = 0
) x=1or 6However,xcannot be 1 as x¡ 3 > 0
) x=6
So, the flagpole is 6 m high.Example 30 Self Tutor
A stone is thrown into the air. Its height above the ground is given by the function
h(t)=¡ 5 t^2 +30t+2metres wheretis the time in seconds from when the stone is thrown.
a How high is the stone above the ground at timet=3seconds?
b From what height above the ground was the stone released?
c At what time is the stone’s height above the ground 27 m?a h(3) =¡5(3)^2 + 30(3) + 2
=¡45 + 90 + 2
=47
) the stone is 47 m above the
ground.b The stone was released whent=0s.
) h(0) =¡5(0)^2 + 30(0) + 2 = 2
) the stone was released from 2 m
above ground level.c Whenh(t)=27,
¡ 5 t^2 +30t+2=27
) ¡ 5 t^2 +30t¡25 = 0
) t^2 ¡ 6 t+5=0 fdividing each term by¡ 5 g
) (t¡1)(t¡5) = 0 ffactorisingg
) t=1or 5
) the stone is 27 m above the ground after 1 second and after 5 seconds.EXERCISE 21J
1 The sum of a number and its square is 110. Find the number.
2 The square of a number is equal to 12 more than four times the number. Find the number.
3 The sum of two numbers is 6 and the sum of their squares is 90. Find the numbers.
4 When a number is subtracted from 2 , the result is equal to the reciprocal of the original number. Find
the number.
5 The base of a triangle is 5 m longer than its altitude. If its area is 33 m^2 , find the length of the base.Quadratic equations and functions (Chapter 21) 449IGCSE01
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Y:\HAESE\IGCSE01\IG01_21\449IGCSE01_21.CDR Monday, 27 October 2008 2:10:14 PM PETER