How do you find all the zeros of #x^3-6x^2+13x-10# with its multiplicities?
We will use the Rational Root Theorem:
If the rational number r/s is a root of a polynomial whose coefficients are integers, then the integer r is a factor of the constant term, and the integer s is a factor of the leading coefficient.
So, the candidates for roots are:
We discover than 2 is a root.
Now we divide the polymorph by (x-2) to discover the other roots:
This second degree polynom is solved with the quadratic formula: