I DID NOT GET THE ANSWER TO THE QUESTION:IF ONE ROOT OF THE POLYNOMIAL 5X^2+13X+K IS RECIPROCAL OF THE OTHER,FIND THE VALUE OF K. PLEASE ELABORATE THE ANSWER IN SIMPLE WORDS

Given equation is: 5x² + 13x + k

Here, Product of the roots is = C/A = k/5

 

Let the roots of equation are a and 1/a, 

So the product of root is ax(1/a) = 1

 

Therefore, k/5 = 1

Thus, k = 5.