If the roots of the equation $6x^2-7x+K=0$ are rational, then is equal to–

Question

If the roots of the equation $6x^2-7x+K=0$ are rational, then is equal to:
$1)$ $-2$
$2)$ $-1,-2$
$3)$ $-2$
$4)$ $1,2$

Welcome to MSE. Please don't post what look like homework questions -- provide some context around the question and tell us what attempts you've made and where you got stuck so we can help you better. This kind of naked question tends to attract downvotes and can get closed. — postmortes, Jan 20 '19 at 18:53

score 0 · Answer 1 · answered Jan 20 '19 at 18:55

0

$\sqrt{7^2-4\times6\times K}$ is rational when $K=1$ or $2$.

answered Jan 20 '19 at 18:55

J. W. Tanner

Or $K=0$ I think ... and I think there is at least one solution for negative $K$ – Mark Bennet Jan 20 '19 at 19:50
Yes, but $K=0$ wasn't one of the choices – J. W. Tanner Jan 20 '19 at 19:51
Well the question is somewhat unclear at the moment and is inadequately specified - negative values are admitted. I can choose an arbitrary integer value of $x$ and then fix $K$ so that this is a root. The other root will then necessarily be rational (sum of roots is rational). (Or I could choose an arbitrary rational value of $x$, though $k$ would likely not be an integer). – Mark Bennet Jan 20 '19 at 19:53

1 Answers1