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

f (x) = x4 - 3x2 - 4

f (x) = x3 + x2 - 4x - 4

Which second degree polynomial function has a leading coefficient of - 1 and root 4 with multiplicity 2?

f (x) = - x2 - 8x - 16

f (x) = - x2 + 8x - 16

f (x) = - x2 - 8x + 16

Which polynomial function has a leading coefficient of 1 and roots 2i and 3i with multiplicity 1

f (x) = (x + 2i) (x + 3i)

f (x) = (x - 2) (x - 3) (x - 2i) (x - 3i)

f (x) = (x + 2i) (x + 3i) (x - 2i) (x - 3i)

In the question "What is the polynomial function of lowest degree with lead coefficient 1 and roots i, - 2, and 2?" The given roots are i, - 2 and 2. Recall that for any polynomial having complex root, the conjugate of the complex root is also a root of the polynomial, thus - i is also a root of the required equation. Thus the required equation is obtainrd thus: f (x) = (x - i) (x + i) (x - 2) (x + 2) = (x^2 + 1) (x^2 - 4) = x^4 - 4x^2 + x^2 - 4 = x^4 - 3x^2 - 4 In the question "Which second degree polynomial function has a leading coefficient of - 1 and root 4 with multiplicity 2?" The required equation is obtained thus: f (x) = - (x - 4) ^2 = - (x^2 - 8x + 16) = - x^2 + 8x - 16 In the question "Which polynomial function has a leading coefficient of 1 and roots 2i and 3i with multiplicity 1" Recall that for any polynomial having complex root, the conjugate of the complex root is also a root of the polynomial, thus - 2i and - 3i are also roots of the required equation. Thus the required equation is obtained thus: f (x) = (x + 2i) (x + 3i) (x - 2i) (x - 3i).