SOLUTION: The Question Is: Find the third-degree polynomial with real coefficients and with zeros 1 and 3+i. The possible answers are: (A)z^3-7z^2+16z-10 (B)z^3+7z^2+16z+10 (C)z^3

Question 30776: The Question Is:
Find the third-degree polynomial with real coefficients and with zeros 1 and 3+i.
The possible answers are:
(A)z^3-7z^2+16z-10
(B)z^3+7z^2+16z+10
(C)z^3-7z^2+4z-10
(D)z^3-5z^2+4z+10
Thanks for your help!

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Find the third-degree polynomial with real coefficients and with zeros 1 and 3+i.
COEFFICIENTS ARE REAL.SO COMPLEX ROUTES SHOULD BE IN CONJUGATES.SO IF 3+I IS A ROOT THEN 3-I IS ALSO A ROOT.SO THE 3 ROOTS ARE
1,3+I AND 3-I..SO THE POLYNOMIAL IS K(X-1){X-(3+I)}{X-(3-I)}=0
(X-1){(X-3)^2-I^2}=0
(X-1)(X^2-6X+9+1)=0
X^3-6X^2+10X-X^2+6X-10=0
X^3-7X^2+16X-10=0..OR IF YOU ARE USING Z THEN
Z^3-7Z^2+16Z-10=0
A IS THE ANSWER

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