Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the function in standard form

Question

2,3,√5

Answer 1

x = sqr5

x^2 = 5

x^2-5 = 0

f(x) = (x-2)(x-3)(x^2-5)

= (x^2 -5x+6)(x^2 -5)

= x^4-5x^3 +x^2 +25x -30