SOLUTION: Find a polynomial f(x) of degree 3 with real coefficients and the following zeros.
-1,3+i
f(x)=
Algebra.Com
Question 450874: Find a polynomial f(x) of degree 3 with real coefficients and the following zeros.
-1,3+i
f(x)=
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
First your real number zero of -1 means:
Hence:
Therefore
is a factor of your polynomial.
Also, by the same logic
)
is also a factor of your desired polynomial
Then, since complex roots always come in conjugate pairs, meaning that if 
is a root of your equation, then 
is also a root of your equation, we can write:
)
is also a factor of your desired polynomial.
Now all you have to do is multiply the three factors:
\left(x\ -\ (3\ -\ i)\right)\left(x\ -\ (3\ +\ i)\right)\ =\ 0)
to find the desired polynomial. Hints: Remember that the product of two conjugates is the difference of two squares and that 
John
My calculator said it, I believe it, that settles it
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