SOLUTION: Suppose that a polynomial function of degree 5 with rational coefficients has the numbers {{{ 1/2 }}} , {{{ 2+ sqrt ( 7 ) }}} , {{{ 1-3i }}} as zeros. Find other zeros. I am not

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Question 288826: Suppose that a polynomial function of degree 5 with rational coefficients has the numbers , , as zeros. Find other zeros.
I am not positive what Degree 5 means, and although I could find the zeros through trial and error, I know there is some process a bit easier, could you show me?
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
A degree of 5 means the highest exponent in the polynomial is 5. The degree also tells you how many roots/zeros it has.

With rational coefficients, the zeros with square roots will come in conjugate pairs: (p+q) and (p-q). This is true because when you multiply (p+q)(p-q) you get which is an expression of perfect squares. This means the square roots will disappear (which needs to happen if there are rational coefficients).

You are given one rational zero, 1/2, and two zeros with square roots:

and
1-3i (Remember that "i" is a square root! It is .)
There are 5 zeros in a polynomial of degree 5 so there two missing zeros. They will be the other "half" of the respective conjugate pairs:

and
1+3i