How to know the multiplicity of roots?

In order to check whether a polynomial has multiple roots or not, you can use the discriminant or the resultant. The discriminant is basically a polynomial in the roots of the polynomial itself, and the resultant is the product of the polynomials in the roots found by the discriminant. If the discriminant and the resultant are 0, then the polynomial has no roots. If the discriminant or the resultant is not equal to 0, then the po

How to know the multiplicity of roots and degree?

The roots of cubic equation are either single, double or triple. The multiplicity of roots can be easily determined by the value of coefficient of x3. If the coefficients of x3 is zero, then the roots are said to be single. If the coefficients of x3 is one, then it will have three solutions. If those roots are all real, they will be all positive, negative or zero. If they are all complex roots, it means that the equation has degenerate roots.

How to find the multiplicity of roots of a polynomial?

If we have a polynomial with more than one real root, it is called a degenerate polynomial. If a polynomial has two distinct real roots, then the function is called bivariate. If a polynomial has three distinct real roots, it is called tridimensional. And if a polynomial has four distinct real roots, then it is called quartic. The next figure shows the graphs of bivariate, tridimensional, and quartic polynom

How to know the multiplicity of roots and coefficents?

If there is one root at the origin, you will get a singular solution. If there are two roots, you will get two roots. If there are three roots, you will get three roots. If there are four roots, you will get four roots. If there are five, six, seven, eight, nine, ten, or more roots, you will get an even number of roots.

How to find multiplicity of roots of a polyn

One simple technique to find the multiplicity of roots of a polynomial is to write the polynomial in the form of a sum of squares of polynomials. For example, if we have a polynomial of the form: $$f(x) = x^3+ax^2+bx+c,$$