Finding and Identifying Roots

I am attempting to write a code that classifies cubic function as simpler, monotone, or neither. To do this I must calculate the derivative of the cubic function and find its roots. So far the code I have is as follows:

%Solicit Data Needed and Display Data

a = input ('Enter a: ');

b = input ('Enter b: ');

c = input ('Enter c: ');

d = input ('Enter d: ');

fprintf ('Cubic Equation: f(x) = ax^3 + bx^2 + cx + d, a = %10.6f, b = %10.6f, c = %10.6f, d = %10.6f\n', a,b,c,d);

%Give error if a = 0

if a == 0

    error ('Please enter a non-zero value for a!')

end

%Print the Derivative of the cubic function

fprintf ('df/dx = 3ax^2 +2bx +c\n');

%Obtain the Roots of the Derivative

r1 = ((-2*b) + sqrt (((2*b)^2 - (4*3*a*c))/(6*a)));

r2 = ((-2*b) - sqrt (((2*b)^2 - (4*3*a*c))/(6*a)));

fprintf ('The first root of the derivative of f is %10.6f\n' , r1);

fprintf ('The second root of the derivative of f is %10.6f\n' , r2);

The equation for the roots should be correct as I have checked it on my calculator and have double checked all the parenthesis, but for some reason when the program is ran the command window displays the wrong values. I don't know why this is occurring. I also need to identify whether the roots are complex and I cant seem to figure out how to do so. Thanks in advance.

Note: I am at a beginner level and have just recently started learning MATLAB...I may be missing something very obvious.

Answer 1

[Star Strider]

The parentheses are not correctly placed.

The entire quantity ‘(-2*b) + sqrt((2*b)^2 - (4*3*a*c)))’ should be divided by ‘(6*a)’:

r1 = ((-2*b) + sqrt((2*b)^2 - (4*3*a*c)))/(6*a);

Correct ‘r2’ similarly.

[Aaron Buell]

Thank you I do not know how I missed that.

[Star Strider]

As always, my pleasure.

No worries. We all do that from time to time.

Answer 2

[madhan ravi]

See roots()