Find all the zeroes of the polynomial p(x)=2x4
-3x3
-3x2+6x-2,If 2 of
the zeroes are √2 − √2.
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Answer:
Answer
The given roots are (x+
2
)(x−
2
)=(x
2
+2)
Then, 2x
4
+7x
3
−8x
2
−14x+8=(x
2
+2)(2x
2
+7x−15)
Now, (2x
2
+7x−15)=2x
2
+10x−3x−15=2x(x+5)−3(x+5)=(2x−3)(x+5)
Then, (x+
2
)(x−
2
)(2x−3)(x+5)=0
x=+
2
,−
2
,−5,
2
3
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