If  be that roots  where ,  such that  and  then the number of integral solutions of λ is

The correct answer is: 3

A quadratic equation, or sometimes just quadratics, is a polynomial equation with a maximum degree of two. It takes the following form:
ax² + bx + c = 0
where a, b, and c are constant terms and x is the unknown variable.
Now we have given  are the roots of equation  where ,  such that  and .
The equation is:

4x²−16x+λ=0

$First\; finding\; the\; discriminant,\; we\; get:$
D=b²-4ac 
Applying it, we get:
D=16²−16λ>0
λ<16...........................(i)
Now, we have sum of roots as: 
we have product of the roots 
Now as per the condition, we have:
 and , multiplying both, we get:

Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, the number of integral solutions of λ is in between