obtain all zeros of x⁴ - x³ -7x²+x+6 of 3 and 1 are zeros
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Step-by-step explanation:
Let f(x)=x
4
+x
3
−23x
2
−3x+60
Given :
3
and −
3
are the zeros of the polynomial.
(x−
3
) and (x−
3
) are factors of f(x)
Divide f(x) by (x
2
−3)
Let f(x)=0
(x
2
+x−20)(x
2
−3)=0
⇒(x
2
+5x−4x−20)(x
2
−3)=0
⇒[x(x+5)−4(x+5)](x
2
−3)=0
⇒(x−4)(x+5)(x+
3
)(x−
3
)=0
Either x=4 or x=−5 or x=
3
or x=−
3
hence all the zeros of the given polynomial are
3
,−
3
,4 and −5.
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