Question

if one root of 5x²+13x+k= 0 is the reciprocal of tha other root,then find value of k.

Answer 1

the eq. is 5x^2+13x+k=0

general form of quadratic eq. is x^2 +(sum of roots)x+(product of roots)=0

divide given eq. by 5

therefore, x^2+13/5x+k/5=0

let the roots be y & 1/y (one root is reciprocal of other)

therefore, product of roots= y*1/y=k/5

so,k=5

Answer 2

Hey

Here is your answer

5x^2+13x+k=0

Let the zeroes be alpha and 1/alpha.

Product of two zeroes= c/a
Alpha x 1/ alpha = k/5
k/5 = 1
k = 5

Hope it helps you!