Question

Which of the following are possible rational roots of the polynomial function? `F(x)= 2x^2-3x+7` `color(white)("d") "A." +/- 7 ;` B. +/- 1/2 C. +/- 1/7 D. +/- 1 E. +/- 2

Which of the following are possible rational roots of the polynomial function?

`F(x)= 2x^2-3x+7`

`color(white)("d") "A."color(white)("d") +- 7`
`color(white)("d")"B."color(white)("d") +- 1/2`
`color(white)("d")"C."color(white)("d") +- 1/7`
`color(white)("d")"D."color(white)("d") +- 1`
`color(white)("d")"E."color(white)("d") +- 2`

Answer 1

None of the offered values are actual solution. However,
the question states `ul("POSSIBLE")` RATIONAL ROOTS
These words do not rule out that they may be wrong

`color(red)("POSSIBLY")rarr x =+-1 and x=+-7`

Explanation:

`color(blue)("The actual roots:")`

Set `y=0=2x^2-3x+7`

Completing the square we have:

`0=2(x-3/4)^2+k+7`

Set `2(-3/4)^2+k=0=>k=-9/8`

`0=2(x-3/4)^2-9/8+7`

`0=2(x-3/4)^2+65/8`

`+-sqrt(-65/16)=x-3/4`

`x=3/4+-sqrt(65/16xx(-1))`

`x=3/4+-sqrt(65)/4 i`

where `x` is part of the 'complex' set of numbers
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Considering the wording of the question")`

However, the question states POSSIBLE ......

These words do not rule out that they may be wrong

`color(brown)("Considering the constant of +7")`

This is a prime number so the only possible structure when considering the constant on its own is:

`(?-1)(?-7)" or "(?+1)(?+7)`

So potentially (not really) `x=+-1 and x=+-7`

As demonstrated above this is not the solution.