Page 304 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

From the graph:
When y = 0 ; x = 3 12
From the graph:
Hence, the solution (or root) of the quadratic
When y = 0 ; x = 3􏰀 􏰁
1
equation 4x2 - 28 + 49 = 0 is x = 3 2 􏰀
Hence, the solution (or root) of the quadratic equation 4􏰂􏰁 - 28 + 49 = 0 is x = 3 Actually, these are two roots but the roots are 􏰁
equal (or coincident).
Actually these are two roots but the roots are equal (or coincident).
Graphical method
Graphical method
Example 5
(c) A graphical method can also be used to solve the quadratic equation r2 + 4r - 21 =
(c) A graphical method can also be used to solve the quadratic equation
0 for a domain, say -8 ≤ r ≤ 4.
􏰄􏰁 +4r-21=0foradomain,say -8􏰅r􏰅4.
FirFsitr,sctocnosntrsutrcutcattabtlaebolefvoafluveaslufoerstfhoerqthueadqruataidcratic equation y = 􏰄􏰁 + 4r – 21 for the equdoatmioaniny-=8 r􏰅2 +r 􏰅4r4–. 21 for the domain -8 ≤ r ≤ 4.
r -8 -7 -6 􏰄􏰁 64 49 36
4r -32 -28 -24 -21 -21 -21 -21
-5 -4 -3 -2 -1 25 16 9 4 1 -20 -16 -12 -8 -4 -21 -21 -21 -21 -21 -16 -21 -24 -25 -24
0 1
0 1 -10 4 -21 -21 -21 -16
2 3 4
4 9 16 8 2 16 -21 -21 -21 -9 0 11
y 11 0 -9
The set of ordered pairs {(-8, 11) , (-7, 0) , (-6, -9) , (-5, -16), (-4, -21), (-3, -24), (-
The set of ordered pairs {(-8, 11) , (-7, 0) , (-6, -9)
2,25), (-1, -24), (0, -21), (1, -16), (2, -9), (3, 0) , (4, 11) } is then used to plot points on
, (-5, -16), (-4, -21), (-3, -24), (-2,25), (-1, -24), (0,
a Cartesian plane; graph paper with axes and scales. A smooth curve is then drawn
-21), (1, -16), (2, -9), (3, 0) , (4, 11) } is then used
connecting the points that were plotted using the set of ordered pairs.
to plot points on a Cartesian plane; graph paper with axes and scales. A smooth curve is then drawn connecting the points that were plotted using the set of ordered pairs.
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