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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-> 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.
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
