Question

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

• A. $5$
• B. $5,6$
• C. $9$
• D. $1,2$

Answer 1

Answer: (D)

$1,2$

Given equation $6x^2-7x+k=0$
For rational roots $D\ge 0$ and $D$ must be perfect square.
$D=49-24k$
Now, we will check the values of k which satisfies above inequality
Option A, gives $D=73>0$ but not perfect square.
Option B is incorrect as already $k\ne -1$ in option A
Option C gives $D=97>0$ but not perfect square.
Option D, for $k=1$, $D=25$ and for $k=2$, $D=1$ which is a perfect square.
Hence, $k=1,2$