Question 140846


Since {{{6}}} and {{{-2/3}}} are given zeros this means that:



{{{x=6}}} and {{{x=-2/3}}}



Get all terms to the left side in each case



{{{x-6=0}}} and {{{3x+2=0}}}



Now use the zero product property in reverse to join the factors.



{{{(x-6)(3x+2)=0}}}



Expand and multiply


{{{3*x^2-16*x-12=0}}}



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Answer:


So the polynomial with roots of  {{{6}}} and {{{-2/3}}} is


{{{3*x^2-16*x-12}}}




Notice how if we graph {{{y=3*x^2-16*x-12}}}, we can visually verify our answer


{{{ graph( 500, 500, -10, 10, -10, 10, 3*x^2-16*x-12 ) }}} Graph of {{{y=3*x^2-16*x-12}}} with roots of {{{x=6}}} and {{{x=-2/3}}}