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which one of the following sets has elements as odd positive integers (a) `S={x in R|x^3-8x^2+19x-12=0}` b) `S={x in R|x^3-9x^2+23x-15=0}` c) `S={x in R|x^3-7x^2+14x-8=0}` d) `S={x in R|x^3-12x^2+44x-48=0}`
A. `S={x inR|x^(3)-8x^(2)+19x-12=0}`
B. `S={x inR|x^(3)-9x^(2)+23x-15=0}`
C. `S={x inR|x^(3)-7x^(2)+14x-8=0}`
D. `S={x inR|x^(3)-12x^(2)+44x-48=0}`

1 Answer

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Best answer
Correct Answer - B
We take option `(a) : x^(3)-8x^(2)+19x-12=0`
`implies(x-1)(x^(2)-7x+12)=0`
`implies(x-1)(x-3)(x-4)=0`
`impliesx=1,3,4`
Thus, it is not a set of elements as odd positive integers.
`(b)x^(3)-9x^(2)+23x-15=0`
`implies (x-1)(x^(2)-8x+15)=0`
`implies(x-1)(x-3)(x-5)=0`
`implies x=1, 3, 5`
Thus, S will be a set of elements as odd positive integers.

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