Question

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

- 5
- 6
- 2
- 3

Hint:

### The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. Here we have to find the number of integral solutions of λ.

## 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:

$4x−16x+λ=0$

$First finding the discriminant, we get:$

D=b^{2}-4ac

Applying it, we get:

D=16^{2}−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:

D=b

^{2}-4ac

Applying it, we get:

D=16

^{2}−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

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