Question

Help! This problem is way too difficult if you can solve it your a lightsaber!

Answer 1

Solution

For what value of x is the polynomial above x-axis:

The roots of the graph passes through -3 and 3

so the value of x above will be:

$(-3,3)\text{ }U\text{ \lparen3,}\infty)$

The reason why the polynomial is having imaginary roots is

Fundamental Theorem of Algebra we explain that a polynomial will have exactly as many roots as its degree (the degree is the highest exponent of the polynomial). So we know one more thing: the degree is 5 so there are 5 roots in total.

The Fundamental Theorem of Algebra assures us that any polynomial with real number coefficients can be factored completely over the field of complex numbers .