Trevor is studying a polynomial function f(x). three given roots of f(x) are -7, 2i, and 7. trevor concludes that f(x) must be a polynomial with degree 3. which statement is true?

a. trevor is correct
b. trevor isn't correct because -2i must also be a root
c. trevor isn't correct because there cannot be an odd number of roots.
d. trevor isn't correct because there cannot be both ration and complex roots

The correct option is: Option (B) Trevor isn't correct because -2i must also be a root

Explanation:
The roots given are: -7, 2i, +7.

We need to differentiate between the real roots and the imaginary roots.

The real roots are: -7 and +7.
The imaginary root given is: 2i

However, the imaginary roots ALWAYS come in pair like 
Because the imaginary roots come from the square root; In this case, the roots might be in the form of: . The square-root of the negative number yields the imaginary numbers (which can be positive or negative), which in this case is +2i and -2i.

Hence the correct answer is that Trevor isn't correct because -2i must also be a root (Option b).

Main idea on left, details on right