Question

Suppose a polynomial of degree 4 with rational coefficients has the given numbers as zeros. Find the other zero.

Answer 1

Answer:

$x_4 = -5 + i$

Step-by-step explanation:

See comment for complete question.

From the complete question, we have:

$Zeros \to -2, -6, -5-i$

Required

Determine the other zero

The zeros can be represented as:

$x_1 = -2$

$x_2 = -6$

$x_3 = -5-i$

Considering the 3rd zero, which is a complex number.

If a polynomial has a complex number as one of its zeros, then its conjugate pair is the corresponding zero

A conjugate pair is given as:

$a + bi$ and $a - bi$

For $x_3 = -5-i$

The conjugate pair is:

$x_4 = -5 + i$

Hence, the other zero is: $-5 + i$