Question 920961
given zeros:{{{sqrt(7)=2.65}}},{{{ -5}}}, and {{{6}}}

find: the polynomial of least degree 


use zero product formula

{{{(x-x[1])(x-x[2])(x-x[3])}}}  substitute {{{x[1]=sqrt(7)}}},{{{x[2]=-5}}}, and {{{x[3]=6}}}

{{{(x-sqrt(7))(x+5)(x-6)}}}

{{{(x^2+5x-sqrt(7)*x-5sqrt(7))(x-6)}}}

{{{x^3-sqrt(7)x^2-x^2+sqrt(7)x-30x+30sqrt(7)}}}...or we can use {{{sqrt(7)=2.65}}} approximately 

{{{x^3-2.65x^2-x^2+2.65x-30x+30*2.65}}}

{{{x^3-3.65x^2-27.35x+79.5}}}

{{{ graph( 600, 600, -10, 10, -10, 90, x^3-3.65x^2-27.35x+79.5) }}}