Question

If you know a root of a function is -2 + the square root of 3i then _____. 2 + the square root of 3i is a possible root. 2 + the square root of 3i is a known root. -2 - the square root of 3i is a possible root. -2 - the square root of 3i is a known root. Just finished the assignment got it wrong but the correct answer is -2 - the square root of 3i is a known root

Answer 1

-2 - Squared 3i is a known root

Explanation:

Answer 2

-2 - the square root of 3i is a known root

Explanation:

we know that

The conjugate root theorem states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a - bi is also a root of that polynomial

we have that

The root of a function is
`-2+√(3)i`

so

Applying the conjugate root theorem

`-2-√(3)i` ---> is also a root of the function

therefore

-2 - the square root of 3i is a known root