from the equation whose roots are1+5√-1, 5-√-1
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Answer:
Given roots are −1±i,−1±
2
(x+1−i)(x+1+i)(x+1−
2
)(x+1+
2
)
=[(x+1)
2
−i
2
][(x+1)
2
−(
2
)
2
]
=(x
2
+2x+1+1)(x
2
+2x+1−2)
=(x
2
+2x+2)(x
2
+2x−1)
=x
4
+2x
3
−x
2
+2x
3
+4x
2
−2x+2x
2
+4x−2
=x
4
+4x
3
+5x
2
+2x−2
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