Data:
f(x) = 0 in x = 2; x = 2; x = - 3
Using the zeros we can form the function as follow:
A zero is the point where the function is 0, if a zero is 2 it means that in x=2 f(x)=0. we can express that like:
[tex]f(2)=0[/tex]and then we can know that it is zero if :
[tex](x-2)=0[/tex]because:
[tex]f(x)=(x-2)\text{ }\Rightarrow f(2)=(2-2)=0[/tex]So using the zeros we form the equations as followç:
[tex]f(x)=(x-2)(x-2)(x+3)[/tex][tex]f(x)=(x^2-4x+2)(x+3)[/tex][tex]f(x)=x^3+3x^2-4x^2-12x+2x+6=x^3-x^2-10x+6[/tex]If we know that the leading coefficient is 3 then:
[tex]f(x)\text{ = 3 (}x^3-x^2-10x+6)[/tex]the final equation is:[tex]f(x)=3x^3-3x^2-30x+18[/tex]