
5-18 Mathematical Methods
choose two numbers a and b such that f ( a) and f ( b)
are of opposite signs so that the graph y = f ( x) crosses
the x-axis between x = a and x = b. This shows that a
root lies between a and b and we have f ( a) f ( b) < 0
(Figure 5.5(b)).
The equation of the chord joining the points
A = (a, f ( a)) and B = (b, f ( b)) is
() ()
() ( )
fb fa
yfb xa
ba
−
−= −
−
(5.21)
The method consists of replacing the curve
y = f ( x) between
A and B by the chord AB and taking
the x-coordinate of the point of intersection of the
chord with the x-axis as an approximation to the root.
Thus a first approximation to the root is given by
1
()