SOLUTION: find a third-degree polynomial equation with rational coefficients that has the roots -5 and 4+i

Question 26803: find a third-degree polynomial equation with rational coefficients that has the roots -5 and 4+i
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
find a third-degree polynomial equation with rational coefficients that has the roots -5 and 4+i
IF THE COEFFICIENTS OF POLYNOMIAL ARE REAL ,THEN COMPLEX ROOTS CAN OCCUR ONLY IN CONJUGATES.SO IF 4+I IS A ROOT THEN 4-I IS ALSO A ROOT.SO,WE HAVE ALL THE 3 ROOTS FOR THE 3 RD. DEGREE POLYNOMIAL...HENCE THE POLYNOMIAL IS GIVEN BY...
(X+5)(X-(4+I))((X-(4-I))=0
(X+5){(X-4)^2-I^2}=0
(X+5)(X^2+16-8X+1)=0
=(X+5)(X^2-8X+17)=0
=X^3-8X^2+17X+5X^2-40X+85=0
=X^3-3X^2-23X+85=0
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