SOLUTION: task: write a polynomial function with rational coefficients in standard form with the given zeros . x= -2,0,radical 3 I'm not sure where to begin .
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Question 303728: task: write a polynomial function with rational coefficients in standard form with the given zeros . x= -2,0,radical 3 I'm not sure where to begin .
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
If a polynomial function has a zero 
, then the polynomial has a factor 
. Also, irrational zeros of polynomial functions with rational coefficients ALWAYS come in conjugate pairs. That means that if 
is a root, then 
is also a root.
So now you know your four zeroes: 2, 0, and , so you can write the four factors of the polynomial:
\ =\ x\left(x\ -\ 2\right)\left(x\ -\ \sqrt{3}\right)\left(x\ +\ \sqrt{3}\right))
The last two give you the difference of two squares, so
\ =\ x\left(x\ -\ 2\right)\left(x^2\ -\ 3\right))
A little FOIL:
\ =\ x\left(x^3\ -\ 2x^2\ -\ 3x\ +\ 6\right))
And then distribute the remaining factor
\ =\ x^4\ -\ 2x^3\ -\ 3x^2\ +\ 6x)
John
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