Answer:
[tex]x^{4}[/tex] - 3x² - 4
Step-by-step explanation:
given the roots of a polynomial, say x = a, x = b and x = c
Then the factors of the polynomial are (x - a), (x - b) and (x - c)
and f(x) = a(x - a)(x - b)(x - c) ← a is a multiplier
Note that complex roots occur in conjugate pairs
hence x = i is a root then x = - i is also a root
the roots are x = - 2, x = 2, x = i and x = - i
factors are (x + 2)(x - 2)(x - i)(x + i) ← expand in pairs
f(x) = (x² - 4)(x² - i²) → (i² = - 1 )
= (x² - 4(x² + 1)
= [tex]x^{4}[/tex] - 4x² + x² - 4 ← collect like terms
= [tex]x^{4}[/tex] - 3x² - 4
