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If 2 is a zero of the function f(x)=6x^(...

If 2 is a zero of the function `f(x)=6x^(3)-11x^(2)-3x+2`, what are the other zeroes ?

A

`-(1)/(3)` and `-(1)/(2)`

B

`-(1)/(3)` and `(1)/(2)`

C

`(1)/(3)` and `-(1)/(2)`

D

`(1)/(3)` and `(1)/(2)`

Text Solution

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The correct Answer is:
C
If 2 is a zero, then x - 2 is a factor. Factor that out of the polynomial `6x^(3)-11x^(2)-3x+2` :
`(6x^(3)-11x^(2)-3x+2)/(x-2)=6x^(2)+x-1`
Now you have a quadratic equation :
`6x^(2)+x-1=0`
`(3x-1)(2x+1)=0`
`3x-1=0` or `2x+1=0`
`x=(1)/(3)` or `-(1)/(2)`
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