The sum of three numbers in A.P. is `-3,` and their product is 8. Find the numbers.

Options

A. 1,2,3
B. -4,-1,2
C. -4,0,1
D. none of these

Answer

B

Explanation

Let the numbers be `(a−d),a,(a+d)`.

Then, Sum of numbers `−3=>(a−d)+a(a+d)=−3=>3a=−3=>a=−1 `

Now,Product of numbers =8

`=>(a−d)(a)(a+d)=8`

`=>a(a^2 −d^2 )=8`

`=>(−1)(1−d^2 )=8 [a=−1]`

`=>d^2=9⟹d=±3`

If `d=3`, the numbers are `−4,−1,2.`
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