Question

How do you write a polynomial function of least degree given the zeros 0, 2, `sqrt3`?

Answer 1

Polynomial function of least degree given zeros `0,2` and `sqrt3` is `x^3-2x^2-sqrt3x^2+2sqrt3x`

Explanation:

A polynomial function of least degree given zeros `alpha,beta` and `gamma` is

`(x-alpha)(x-beta)(x-gamma)`

Hence, a polynomial function of least degree given zeros `0,2` and `sqrt3` is

`x(x-2)(x-sqrt3)`

= `x(x^2-2x-sqrt3x+2sqrt3)`

= `x^3-2x^2-sqrt3x^2+2sqrt3x`