Question 1004102

Find a polynomial function of 
degree 4 with 
{{{x[1]=-1}}} as a zero of multiplicity {{{3}}}, 
{{{x[2]=0}}} as a zero of multiplicity {{{1}}}

use zero product formula:

{{{f(x)=(x-x[1])(x-x[1])(x-x[1])(x-x[2])}}}

{{{f(x)=(x-(-1))(x-(-1))(x-(-1))(x-0)}}}

{{{f(x)=(x+1)(x+1)(x+1)(x)}}}

{{{f(x)=(x^2+x+x+1)(x+1)(x)}}}

{{{f(x)=(x^2+2x+1)(x^2+x)}}}

{{{f(x)=x^4+2x^3+x^2+x^3+2x^2+x}}}

{{{f(x)=x^4+3x^3+3x^2+x}}}


{{{ graph( 600, 600, -5,5, -5, 10, x^4+3x^3+3x^2+x) }}}