MTH3051 Introduction to Computational Mathematics - User Web ...

School of Mathematical Sciences
Monash University
What more do we need to make this code work?
We need values for a,b and c. This is easy – we simply include lines like a = 2; b =
1; c = 5; before the above pair of lines.
What can go wrong with this code?
We might encounter complex roots. Though Matlab can handle complex numbers (without
any fuss) we’ll declare (for this example) that complex roots are forbidden. So we
need to avoid computing the square root when b 2 − 4ac < 0. This we do by using an if
statement.
Here is our updated code.
a = 2; b = 1; c = 5;
if ( b*b - 4*a*c >= 0 )
r_1 = ( -b + (b*b - 4*a*c)^(1/2) )/(2*a) ;
r_2 = ( -b - (b*b - 4*a*c)^(1/2) )/(2*a) ;
end
Notes
◮ The ; also allows us to put more than one expression on each line.
◮ The if (...) and end lines define the block of lines to be executed only when
b 2 − 4ac is greater or equal to zero.
If we left the code as it is we could run into another problem further down the track.
How so?. Well, we have deliberately chosen (or forgotten?) to not set the values for r 1
and r 2 in the case of complex roots. But what would happen if we tried to use r 1 and
r 2 later, in some other part of the code? Heaven only knows what values would be used
(never assume that a variable starts with an initial value of zero). Clearly we need to
provide values for r 1 and r 2 for all possible cases. Thus we modify the if statement
as follows
a = 2; b = 1; c = 5;
if ( b*b - 4*a*c >= 0 )
r_1 = ( -b + (b*b - 4*a*c)^(1/2) )/(2*a) ;
r_2 = ( -b - (b*b - 4*a*c)^(1/2) )/(2*a) ;
else
r_1 = 0;
r_2 = 0;
end
Note that setting r 1 = 0 and r 2 = 0 is mathematically wrong but at least we can
now proceed with known values for r 1 and r 2. We could also use these zero values as
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