If one zero of the polynomial f(x)=(k² + 4)x² + 13x + 4k is reciprocal of the other zero, then value of k is :

Correct option is C

Solution:

Given:

The polynomial is f(x) = $$(k^2 + 4)x^2 + 13x + 4k$$​ . One zero of the polynomial is the reciprocal of the other.

Condition for Reciprocal Roots:

If one root is the reciprocal of the other, the product of the roots is:

$$\text{Product of roots} = 1$$​​

For a quadratic polynomial $$ax^2 + bx + c$$​ , the product of the roots is:

$$\text{Product of roots} = \frac{c}{a}$$​​

Coefficients of the Polynomial:

Coefficient of $$x^2 : a = k^2 + 4$$​
 Constant term: c = 4k

Substitute these values into the condition:

$$\frac{c}{a} = 1$$​​

Solve for k :

$$\frac{4k}{k^2 + 4} = 1$$​​

Multiply through by $$k^2$$​ + 4 (assuming $$k^2 + 4 \neq 0$$​ ):

4k = $$k^2$$​ + 4

Rearrange:

$$k^2$$​ - 4k + 4 = 0

Factorize:

$$(k - 2)^2$$​= 0

Solve:

k = 2

Final Answer:

Option C: 2