[tex]f(x)=x^2-(2+\sqrt 3)x+2\sqrt3[/tex]
Solution:
Given zeros are [tex]2,\sqrt 3[/tex].
If a is zero of f(x), then (x – a) is a factor of f(x).
So, [tex](x-2)[/tex] and [tex](x-\sqrt 3)[/tex] are factors of f(x).
On multiplying factors, we get the polynomial function.
[tex](x-2)(x-\sqrt 3)=x^2-2x-\sqrt 3x+2\sqrt3[/tex]
Combine like terms together.
[tex](x-2)(x-\sqrt 3)=x^2-(2+\sqrt 3)x+2\sqrt3[/tex]
Degree of the polynomial is 2.
A leading coefficient is 1.
Hence the polynomial [tex]f(x)=x^2-(2+\sqrt 3)x+2\sqrt3[/tex].
