Question

If the roots of the equation $6x^2-7x+k=0,k>-3$ are rational, then possible integral value(s) of $k$ is/are

• A. $-1$
• B. $-1,-2$
• C. $-2$
• D. $0,1,2$

Answer 1

The correct option is D $0,1,2$

If roots are rational, then
$\Delta \ge 0$ should be a perfect square.
$49-24k\ge 0$
$\Rightarrow k\le \frac{49}{24}$

For $k=0$
$\Delta =49$, which is a perfect square
For $k=1$,
$\Delta =25$, which is a perfect square.
For $k=-1$,
$\Delta =73$, not a perfect square
For $k=2$,
$\Delta =1$, which is a perfect square.
For $k=-2$,
$\Delta =97$, not a perfect square