If one root of the equation $$(k + 1)x^2 - 13kx + 7 - 2k = 0$$​ is the reciprocal of the other, then the value of k
is:

Correct option is B

Given:

The quadratic equation is:

​$$(k+1)x^2 - 13kx + 7 - 2k = 0$$​​

It is given that one root is the reciprocal of the other.

Concept Used:

If the roots of a quadratic equation are α and $$\frac{1}{\alpha}$$​​, then the product of the roots is always 1.
For a quadratic equation of the form $$ax^2 + bx + c = 0$$​, the product of the roots is given by:

​$$\alpha \cdot \frac{1}{\alpha} = \frac{c}{a} = 1$$​​

Solution:

From the given equation:

a = (k+1)

b = -13k

c = 7 - 2k

Now,

​$$\frac{c}{a} = 1$$​​

​$$\frac{7 - 2k}{k+1} = 1$$​​

7 - 2k = k + 1

7 - 1 = k + 2k

6 = 3k

k = 2