Question 1170234

given:

The polynomial of degree {{{5}}}, 
{{{P(x)}}} has leading coefficient {{{1}}},
has roots of multiplicity {{{2}}} at {{{x = 2 }}}and {{{x = 0}}} ,so roots are:

{{{x[1] = 2}}}
{{{x[2] = 2}}}
{{{x[3] = 0}}}
{{{x[4] = 0}}}

 and
 also given a root of multiplicity 1 at {{{x = -2 }}} => 

{{{x[5] =-2}}}


{{{P(x)=(x-x[1])(x-x[2])(x-x[3])(x-x[4])(x-x[5])}}}

{{{P(x)=(x-2)(x-2)(x-0)(x-0)(x-(-2))}}}

{{{P(x)=(x-2)(x-2)(x)(x)(x+2)}}}

{{{P(x)=x^2(x-2)(x^2-2^2)}}}

{{{P(x)=(x^3-2x^2)(x^2-4)}}}

{{{P(x)=x^5 - 2x^4 - 4x^3 + 8x^2}}}