Question 1003893

a polynomial of lowest possible degree that has {{{x[1]=2}}} as a zero of multiplicity 3, and {{{x[2]=-1}}} as a zero of multiplicity 1

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

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

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

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

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

{{{f(x)=x^4-5x^3+6x^2+4x-8}}}


{{{ graph( 600, 600, -15, 15, -15, 15, x^4-5x^3+6x^2+4x-8) }}}