Extra value in my work

function MyRoots = MyCubicRoot(a_3,a_2,a_1,a_0)
a = a_2/a_3;
b = a_1/a_3;
c = a_0/a_3;
Q = (a^2 - 3*b)/9;
R = (2*a^3 - 9*a*b +27*c)/54;
d = R^2 - Q^3;
if d < 0
    t = acos(R/sqrt(Q^3));
    x_1 = -(a/3)-2*sqrt(Q)*cos(t/3);
    x_2 = -(a/3)-2*sqrt(Q)*cos((t+2*pi)/3);
    x_3 = -(a/3)-2*sqrt(Q)*cos((t+4*pi)/3);
    
    Order = [x_1,x_2,x_3];
    MyRoots = sort(Order,'ascend');
    
    disp('The polynomial 1x^3-6x^2+11x-6 has three real roots given by')
    disp(x_1)
    disp(x_2)
    disp(x_3)
    
elseif abs(d) < 1e-6
    x_1 = -(a/3) + 2*nthroot(-R,3);
    x_2 = -(a/3) - nthroot(-R,3);
    
    
    MyRoots = sort(x_1,x_2);
    
    disp('The polynomial 2x^3+9.8x^2-4.9x-51.45has distinct real roots given by')
    disp(x_1)
    disp(x_2)
    
else
    x_1 = -(a/3)+nthroot(-R+sqrt(d),3)+nthroot(-R-sqrt(d),3);
    
    MyRoots = x_1;
    
    disp('The polynomial x^3-7.8693x^2+13.377x-6.5354 has only real root given by')
    disp(x_1)
end
end

The polynomial 1x^3-6x^2+11x-6 has three real roots given by

1

3

2

myRoots =

1 2 3

The polynomial 1x^3-6x^2+11x-6 has three real roots given by

-3.5000

2.1000

-3.5000

myRoots =

-3.5000 -3.5000 2.1000

The polynomial x^3-7.8693x^2+13.377x-6.5354 has only real root given by

5.7357

myRoots =

5.7357

I get an extra -3.5 how do I get rid of it

[KSSV]

roots of which polynomial?

[Yogesh Bhambhwani]

this one

2 x^3 + 9.8 x^2 - 4.9 x - 51.45 = 0

a_3 = 2; a_2 = 9.8; a_1 = -4.9; a_0 = -51.45;

myRoots = MyCubicRoot(a_3,a_2,a_1,a_0)

Im only suppse to get one -3.5 but I get two of them in my answer

[Dyuman Joshi]

You are getting 2 values because it is a repeated root. You can use unique() to get rid of the repeated value.

[Yogesh Bhambhwani]

I tried what you said and it didnt work

[Dyuman Joshi]

Use this unique(roots(input))

Answer 1

[Jemima Pulipati]

Hello,

From my understanding, x_1 and x_3 are not exactly the same values.

You can verify this by changing the preferences of how the numeric format is displayed. Go to Preferences -> Command Window -> Set the 'Numeric Format' under 'Text Display' to 'long e'. Now if you try to print those values it does not show them to be the same. Since they have a slight difference, they are treated as different numbers and unique() is displaying all the three numbers in the answer.

If you still do not want to consider that minor difference and remove one of them, you may consider using uniquetol(). This searches for unique values within a given tolerance value.