Answer:
1
Step-by-step explanation:
For a quadratic equation, the roots are expressed by the quadratic formula.
x=(-b+/- Sqrt[b^2-4ac])/2a
In this case a=6, b=-7 and c=k
So,
x=(7 +/- √[(-7)^2-4(6)(k)]/2(6))
Simplifying gives:
x=(7 +/- √[49-24k])/12
For k=0 the square root simplifies to √[49]=7 which yields roots of 7/6 and 0
For k=1 the square root simplifies to √[49-24]=√[25]=5 which yields roots of 1 and 1/6
For k=2 the square root simplifies to √[49-48]=√[1]=1 which yields roots of 2/3 and 1/2
k= 1 as other roots are fractions
