Option B
Trevor isn't correct because -2i must also be a root
Solution:
For the polynomial with roots -7, 2i and 7 their roots can be,
1. ) Real roots
2.) Imaginary roots
The real roots are: -7 and +7
The imaginary root given is: 2i
The imaginary roots come from the square root. So they will be in form of [tex]\pm 2i[/tex]
Therefore,
For f(x) with roots -7 and +7 and [tex]\pm 2[/tex] we have,
[tex]f(x)=a(x+7)(x-7)(x-2i)(x+2i)[/tex]
Fundamental Theorem of Algebra states that a polynomial will have exactly as many roots as its degree (the degree is the highest exponent of the polynomial).
So for f(x) with 4 roots, degree of f(x) is 4
So option B is correct. Trevor is not correct because –2i must also be a root.
