1
Week 2
MECH201
Roots of Equations
Chapter 5-8
Week 2
Objectives
•
Understanding what roots problems are
and where they occur in engineering and
science
•
Knowing how to determine a root
graphically
•
Knowing how to solve a roots problem
using bracketing methods
•
Knowing how to solve a roots problem
with open methods
Week 2
What are roots?
• The values that make equation
equal to zero. (
zeros
of equations)
• Eg.
are the roots
of equation
a
ac
b
b
x
2
4
2
−
±
−
=
( )
0
2
=
+
+
=
c
bx
ax
x
f
Week 2
Solution Methods
•
Some equations have analytical solutions
•
But many equations can not be solved directly
or analytically
•
One method is the
graphical method
to plot the
function and determine where it crosses the x-
axis, the point of crossing is the root
•
Although the graphical methods are useful, it is
limited because of their lack of precision

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