find the third polynomials that has zeros at xvalues 33 and

find the third polynomials that has zeros at x-values 3,-3 and 0 and whose x-term has coefficient of 54.

Solution

let f(x) be polynomials

f(x)=a(x-x1)(x-x2)(x-x3)

here xi=3,x2=-3,x3=0 and a=54

so f(x)=54(x-3)(x+3)(x-0)

f(x)=54(x^2-9)x

f(x)=54(x^3-9x)

f(x)=54x^3-486x