Question 1080409
Find a polynomial {{{f(x)}}} of degree {{{4}}} that has the following zeros:
{{{x[1]=-3}}},{{{x[2]=6}}},{{{x[3]=0}}},{{{x[4]=7 }}}

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

{{{f(x)=(x-(-3))(x-6)(x-0)(x-7)}}} 

{{{f(x)=(x+3)(x-6)(x)(x-7)}}}

{{{f(x)=(x^2-6x+3x-18)(x^2-7x)}}}

{{{f(x)=(x^2-3x-18)(x^2-7x)}}}

{{{f(x)=x^4 -10x^3 + 3x^2 + 126x}}}


{{{f(x)=x(x + 3)(x - 6)(x - 7)}}}


check zeros:

{{{ graph( 600, 600, -25, 25, -130, 130,x^4-10x^3+3x^2+126x) }}}