Answered

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

Sagot :

Answer:

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

Step-by-step explanation:

Complex roots:

I a complex number [tex]a + bi[/tex] is a root of a polynomial, it's conjugate [tex]a - bi[/tex] 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.

s139297

Answer:

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

Step-by-step explanation:

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