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Firdavs [7]
2 years ago
7

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

Mathematics
1 answer:
Sauron [17]2 years ago
7 0

Answer:

f(x) has two imaginary roots and one real root.

Step-by-step explanation:

Complex roots:

I a complex number a + bi is a root of a polynomial, it's conjugate a - bi is also a root.

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

This means that -5 - 2i is another root of the polynomial, and thus, 2 of the roots are complex.

Third degree, so it has three roots, which means that the third root is real(not possible to have a complex root without it's conjugate), and thus, the correct answer is:

f(x) has two imaginary roots and one real root.

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