polynomial in standard form that has the following characteristics.

Question

leading coefficient: -1/2

zeros: -6, -2, -i

Answer 1

Since -i is a root, so is i.

A possible polynomial is (-1/2)(x+6)(x+2)(x-i)(x+i)

= (-1/2)(x²+8x+12)(x²+1) = -1/2(x⁴+x²+8x³+8x+12x²+12)

= (-1/2)x⁴ - 4x³ - (13/2)x² - 4x - 6