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Find a cubic polynomial whose zeroes are...

Find a cubic polynomial whose zeroes are `(1)/(2),-(3)/(2)` and 2.

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The correct Answer is:
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Let `" " alpha=(1)/(2),beta=-(3)/(2)` and `gamma=2`
`:. " " alpha+beta+gamma=(1)/(2)-(3)/(2)+2=1`
`alphabeta+betagamma+gammaalpha=((1)/(2))(-(3)/(2))+(-(3)/(2))(2)=(-3)/(4)-3+1=-(11)/(4)`
and `" " alphabetagamma=((1)/(2))(-(3)/(2))(2)=-(3)/(2)`
`:. ` Cubic polynomial `=x^(3)-(alpha+beta+gamma)x^(2)+(alphabeta+betagamma+gammaalpha)x-alphabetagamma`
`=x^(3)-x^(2)-(11)/(4)x-(3)/(2)~~4x^(3)-4x^(2)-11x-6 " "` Ans.
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