One root of a third degree polynomial function f(x) is –5 + 2i. Which statement describes the number and nature of all roots for this function?

Given :

One root of a third degree polynomial function f(x) is –5 + 2i.

To Find :

The number and nature of all roots for this function.

Solution :

We know, there are exactly three roots in any third degree polynomial.

Also, we know complex roots always comes in pair i.e. the other root is the conjugate of each other .

So, other root is , -5 - 2i .

Also, since complex roots come in conjugate pair. So, third root cannot be complex.

Therefore, 2 roots are complex and 1 is real.

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute: