Showing that a equation has no rational roots

[mwok]

Show that equation f(x) = 2x^5 + 3x^3 + 7 has no rational root.

I conducted a rational roots test which revealed all possible zeroes as:
+/- 1,7 divided by 1,2

So that reveals that the possible roots are: 1, 1/2, 7, 7/2, -1, -1/2, -7, -7/2

None of those produce a zero value when plugged into the equation above and thus, the equation has no rational roots. Am I correct?

 

[Deleted member 4993]

Show that equation f(x) = 2x^5 + 3x^3 + 7 has no rational root.

I conducted a rational roots test which revealed all possible zeroes as:
+/- 1,7 divided by 1,2

So that reveals that the possible roots are: 1, 1/2, 7, 7/2, -1, -1/2, -7, -7/2

None of those produce a zero value when plugged into the equation above and thus, the equation has no rational roots. Am I correct?..........Yes