Question

Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots

V5 and 2?

Answer 1

f(x) =
`3x^(3) - 6x^(2) - 15x + 30`

Explanation:

If
`√(5)` is a root, then so is -
`√(5)`

f(x) = 3(x +
`√(5)`)(x -
`√(5)`)(x - 2)

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

= 3(
`x^(3) - 2x^(2) - 5x + 10`)

=
`3x^(3) - 6x^(2) - 15x + 30`