Question

Find a polynomial function of lowest degree with rational coefficients that has the

given numbers as some of its zeros.
√3,51
The polynomial function in expanded form is f(x) =

Answer 1

Answer:
`f(x)=x^3 -51x^2 -3x+153`

Explanation:

By the conjugate root theorem, the roots are
`√(3), -√(3), 51`.

Letting the leading coefficient be 1,

`f(x)=(x-√(3))(x+√(3))(x-51)\\\\=(x^2 -3)(x-51)\\\\=x^3 -51x^2 -3x+153`