SOLUTION: Write a polynomial function with rational coefficients in standard form with the given zeros. 2-i, square root of 5

Question 940564: Write a polynomial function with rational coefficients in standard form with the given zeros. 2-i, square root of 5
Found 2 solutions by MathLover1, KMST:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
given zeros:
, if given there must be too because complex roots always come in pairs

to find a polynomial function use zero product rule:
plug in given zeros

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If the polynomial must have real coefficients ,
having an imaginary root requires
also having the conjugate imaginary number as a root.
If the polynomial has an irrational root,
to have rational coefficients,
it must also have the conjugate irrational number as a root.
So your polynomial must have as roots
, , , and .
The simplest one would be

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