Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and given 2, 3, and square root of 7.

Question

Don’t get how to do it or how to come by an answer

Answer 1

To have rational coefficients, -√7 must also be a root, so the roots are

2

3

√7

-√7

Then

f(x) = (x - 2)(x - 3)(x - √7)(x + √7)