The polynomial of degree 5,

Question

The polynomial of degree 5,  has leading coefficient 1, has roots of multiplicity 2 at  and , and a root of multiplicity 1 at Find a possible formula for .

 

Answer 1

(x-2)^2(x^2)(x+4) is the polynomial with zeros 2, 0, and-4, where 2 and 0 have multiplicity 2

= x^2(x^2 -4x +4)(x+4)

=x^2(x^3 -12x +16)

= x^5 -12x^3 +16x^2 5th degree polynomial with the given zeros