Find all the zeros of the polynomial (2x4 - 11x + 7x + 13x - 7), it being given that two of its zeros are (3 + 2) and (3 - 12).
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Let f(x)=2x
4
−11x
3
+7x
2
+13x−7
Given : (3+
2
) and (3−
2
) are the zeroes of f(x)
So (x−(3+
2
)) and (x−(3−
2
)) are factors of f(x)
and (x−(3+
2
))(x−(3−
2
))=x
2
−6x+7 is a factor of f(x)
Divide f(x) by x
2
−6x+7 we get
set f(x)=0
2x
4
−11x
3
+7x
2
+13x−7=0
(x
2
−6x+7)(2x
2
+x−1)=0
(x−(3−(
2
))(x−(3+
2
))(2x−1)(x+1)=0
x=3−
2
or x=3+
2
or x=
2
1
or x=−1
hence all the zeros of the given polynomial are (−3−
2
),(−3+
2
),
2
1
and−1.
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