Question

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

Answer 1

Answer:

P(x) = $x^{4}$ - 7x² + 12

Step-by-step explanation:

Given zeros x = 2, x = - 2, x = $\sqrt{3}$, x = - $\sqrt{3}$

Then the factors are (x - 2), (x + 2), (x - $\sqrt{3}$ ), (x + $\sqrt{3}$ )

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

P(x) = (x - 2)(x + 2)(x - $\sqrt{3}$ )(x + $\sqrt{3}$ ) ← expand in pairs using FOIL

      = (x² - 4)(x² - 3) ← distribute

     = $x^{4}$ - 3x² - 4x² + 12 ← collect like terms

    = $x^{4}$ - 7x² + 12