Question

Is it possible for a sixth degree polynomial function with integer coefficients to have no real zeroes? Choose all that apply: Yes No

Answer 1

Using the Factor Theorem, it is found that yes, it is possible for a sixth degree polynomial function with integer coefficients to have no real zeroes, as they can have three complex-conjugate pairs.

What is the Factor Theorem?

The Factor Theorem states that a polynomial function with roots $x_1, x_2, \codts, x_n$ is given by:

$f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)$

In which a is the leading coefficient.

If a complex number is a root of a function, it's conjugate will also be a root. Thus, with three pairs of complex-conjugate roots, for example, $\pm i, \pm 2i, \pm 3i$, a sixth degree function with no real zeros is formed, so the answer is Yes.

More can be learned about the Factor Theorem at brainly.com/question/24380382