Question

if one root of equation 5x+13x+k=0 is reciprocal of the other root then the value of k is

Answer 1

let roots be a and 1/a
so a x 1/a = k/5
1 = k/5
k = 5

Answer 2

Let one root of the given polynomial be Alpha.


Given that other zero is Reciprocal the one zero.


So,

Other zero = 1/Alpha.

Given polynomial is 5X² + 13X + K.

Here,

A = Coefficient of X²


B = Coefficient of X


And,

C = Constant term.




As we know that,

Product of zeroes = C/A

Alpha × 1/Alpha = K/5

1 = K/5

K = 5