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If 2 is a zero of the polynomial x^(3)-2...

If 2 is a zero of the polynomial `x^(3)-2x^(2)-x+2`, then find its other zeroes.

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The correct Answer is:
N/a
Let`" " p(x)=x^(3)-2x^(2)-x+2`
`:' " " x=2` is a zero of p(x)
`:.` (x-2) is a factor of p(x)

Polynomial
`:. " p(x)=x^(3)-2x^(2)-x+2=(x-2)(x^(2)-1)=(x-2)(x^(2)-1^(2))`
`=(x-2)(x-1)(x+1)`
Now, `" "p(x)=0`
`implies (x-2)(x-1)(x+1)=0`
`implies " " x-2=0" " or " " x+1=0`
`implies" "x=2 " " or " " x=1 " or " x=-1`
Hence, other zeroes are 1 and -1.`" "` Ans.
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