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

User Azr
by
8.2k points

1 Answer

3 votes

Answer:

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

User Ranee
by
8.5k points

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