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

Question

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

anonymous · Answer

:|  Your attempt?

anonymous · Answer

When I first did it, I got b. I'm deciding between b and d.

kc_kennylau · Answer

Your first attempt is correct

kc_kennylau · Answer

A polynomial can have both rational and complex roots

kc_kennylau · Answer

For example, (x-2)(x^2+4) have roots 2, 2i and -2i

anonymous · Answer

Awesome! I wasn't sure, I guess I just needed confirmation. Thank you thank you thank you!

kc_kennylau · Answer

no problem :)