Question

HELP NEEDED URGENTLY!!!

What is the polynomial function of lowest degree with lead coefficient 1 and roots i, –2, and 2?



f(x) = x3 – x2 – 4x + 4

f(x) = x4 – 3x2 – 4

f(x) = x4 + 3x2 – 4

f(x) = x3 + x2 – 4x – 4

Answer 1

I suppose you mean roots + or - i, -2 and 2.
f(x) = (x + i)(x - i)(x + 2)(x - 2) = (x^2 + 1)(x^2 - 4) = x^2(x^2 - 4) + (x^2 - 4) = x^4 - 4x^2 + x^2 - 4 = x^4 - 3x^2 - 4