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If sum of zeroes of a polynomial =alpha+...

If sum of zeroes of a polynomial `=alpha+beta=-8` and product of zeroes `=alphabeta=6`, then form a polynomial whose zeroes are `(alpha-beta)` and `(alpha+beta)`.

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The correct Answer is:
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Since, `alpha+beta=-8` and `alpha beta=6`
`:. " "(alpha-beta)^(2)=(alpha+beta)^(2)-4alphabeta=(-8)^(2)-4(6)=64-24=40`
`:. " " alpha-beta=+-2sqrt(10)`
If `(alpha-beta)` and `(alpha+beta)` are zeroes of a polynomial, then polynomial is
`k[x^(2)-{(alpha-beta)+(alpha+beta)}x+(alpha-beta)(alpha+beta)`
`=k[x^(2)-{+-sqrt(10)-8}x+-2sqrt(10)(-8)]=k[x^(2)+(8+-2sqrt(10)x+-16sqrt(10)] " "` Ans.
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