Question 1008060

Degree {{{4}}};    
zeros: {{{x[1]=-1}}}, {{{x[2]=0}}},{{{x[3]= 4}}},{{{x[4]= 1/4}}} 
coefficient of {{{x^3}}} is {{{13}}}

{{{f(x)=ax^4+13x^3+cx^2+dx+e}}}

{{{(x-x[1])(x-x[2])(x-x[3])(x-x[4])=0}}}

{{{(x+1)(x-0)(x-4)(x-1/4)=0}}}

{{{(x^2+x)(x-4)(x-1/4)=0}}}

{{{(x^3+x^2-4x^2-4x)(x-1/4)=0}}}

{{{(x^3-3x^2-4x)(x-1/4)=0}}}

{{{x^4-3x^3-4x^2   -(1/4)x^3+3x^2(1/4)+4(1/4)x=0}}}

{{{x^4-3x^3 -x^3/4+3x^2/4-4x^2+x=0}}}

{{{x^4-12x^3/4 -x^3/4+3x^2/4-16x^2/4+x=0}}}

{{{x^4-13x^3/4 -13x^2/4+x=0}}}.....multiply all terms by {{{4}}}

{{{4x^4-4(13x^3)/4-4(13x^2)/4+4x=0}}}

{{{4x^4-13x^3-13x^2+4x=0}}}  

so, your polynomial is:

{{{f(x)=4x^4-13x^3-13x^2+4x}}} 

{{{ graph( 600, 600, -5, 5, -10, 10,4x^4-13x^3-13x^2+4x) }}}