MATLAB: How would i type in the fraction in the polynomial to find the real and complex roots

roots

   fx = x^5-((x^4)/2)-2x^3-x^2-3
roots = fx

Best Answer

I expanded your function in the Symbolic Math Toolbox, and got the coefficient vector:

cfx = [1     -0.5       -2       -1        0       -3];
fxroots = roots(cfx)

produces:

fxroots =
       1.9710e+000 +             i
      -1.1131e+000 +654.8187e-003i
      -1.1131e+000 -654.8187e-003i
     377.6052e-003 +877.5463e-003i
     377.6052e-003 -877.5463e-003i

Note that the first root is real. It should be simply 1.9710, but since the others are complex, it is listed with a complex part for consistency. You could do all of this in the Symbolic Math Toolbox of course, but since you didn’t mention that you have access to it, I do not assume you do.

Related Solutions

MATLAB: Real Roots of a Polynomial

Use 'roots' to find the roots of polynomials.

 r = roots([1,7,-8,5,1]); % Get all the roots
 r = r(imag(r)==0); % Save only the real roots

The 'isreal' function is true only if All elements of a vector are real, so it isn't appropriate for sorting out the real roots.

A polynomial with all real coefficients such as yours cannot have an odd number of complex roots. They must occur in conjugate pairs. As you see, in your particular polynomial there are just two complex roots, which are conjugates of one another.

MATLAB: Mag_curve_1 how to plot

When I define your data as:

M = [-1.8000000e+003 -1.3000000e-003 
   -1.7640000e+003 -1.2956598e-003 
   -1.7280000e+003 -1.2916738e-003 
   -1.6920000e+003 -1.2879611e-003
                . . .
    0.0000000e+000  0.0000000e+000 
    3.6000000e+001  9.2857143e-005];

and plot it:

figure(1)
plot(M(:,1), M(:,2))
grid

it plots a single curve.

Best Answer

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MATLAB: Real Roots of a Polynomial

MATLAB: Mag_curve_1 how to plot

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