Question 47011: use the given root to find the solution set of the polynomial equation
x4-45x2-196=0 : 2i
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! use the given root to find the solution set of the polynomial equation
F=x4-45x2-196=0 : 2i.SINCE THE EQN.HAS REAL COEFFICIENTS ,IF 2I IS A ROOT ,ITS CONJUGATE -2I IS ALSO A ROOT.SO
LET G=(X+2I)(X-2I)=X^2-4I^2=X^2+4 IS A FACTOR.DIVIDING F WITH G
X^2+4)X^4-45X^2-196(X^2-49
......X^4+4X^2
-------------------------
..........-49X^2-196
..........-49X^2-196
------------------------------
..............0................
SO QUOTIENT IS X^2-49=(X)^2-7^2=(X+7)(X-7)
HENCE F=(X+2i)(X-2I)(X+7)(X-7)
SOLUTION SET IS 2I,-2I,7,-7
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