Question

Find a polynomial P(x) with the zeros x=2, −(2), √3, −√3

Answer 1

P(x) =
`x^(4)` - 7x² + 12

Explanation:

Given zeros x = 2, x = - 2, x =
`√(3)`, x = -
`√(3)`

Then the factors are (x - 2), (x + 2), (x -
`√(3)` ), (x +
`√(3)` )

and the polynomial is the product of the factors, that is

P(x) = (x - 2)(x + 2)(x -
`√(3)` )(x +
`√(3)` ) ← expand in pairs using FOIL

= (x² - 4)(x² - 3) ← distribute

=
`x^(4)` - 3x² - 4x² + 12 ← collect like terms

=
`x^(4)` - 7x² + 12