SOLUTION: Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. -1,3+i f(x)=

Algebra ->  Equations -> SOLUTION: Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. -1,3+i f(x)=       Log On


   

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) About Me  (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:



to find the desired polynomial. Hints: Remember that the product of two conjugates is the difference of two squares and that

John

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