SOLUTION: Suppose that a polynomial function of degree 5 with rational coefficients has 2-3i, -5 and the square root of 7 as zeros. Find the other zeros. I am having a terrible time with

SOLUTION: Suppose that a polynomial function of degree 5 with rational coefficients has 2-3i, -5 and the square root of 7 as zeros. Find the other zeros. I am having a terrible time with

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Question 428149: Suppose that a polynomial function of degree 5 with rational coefficients has 2-3i, -5 and the square root of 7 as zeros. Find the other zeros.
I am having a terrible time with this problem. I understand the degree of 5 means there are five zeros. I believe the answer is 2+3i and - square root of 7. Help me step by step this please.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Your answer is exactly correct. For a polynomial equation with real coefficients, complex roots always occur in conjugate pairs. The irrational conjugate roots theorem says: Let

be any polynomial with rational coefficients. If

is a root of

, where

is irrational and

and

are rational, then another root is

.

So, if you have a complex root

then you are guaranteed to have another complex root

. Likewise, if you have an irrational root

where

and

, then you are guaranteed to have another irrational root

Therefore

is a root guarantees that

is a root and

guarantees

John

My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

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