Question

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

Answer 1

Given equation: 5x²+13x+k=0

Given that one zero is reciprocal of the other.

Let one zero be a
Other zero = 1/a

We know that product of zeroes (of polynomial ax²+bx+c) = c/a

=> a × 1/a = k/5

=> 1 = k/5

=> k = 5

Hence, k = 5

Answer 2

hey there!! here is your answer

let One of the root =
$\alpha \: so \: other \: root \: = \frac{1}{ \alpha }$

given quadratic equation

$5 {x}^{2} + 13x + k = 0$

we know, product of zeros = c/a

$\frac{k}{5} = \alpha \times \frac{1}{ \alpha }$

$\frac{k}{5} = 1$

$k = 5 \times 1 = 5$

so the value of k is 5

hope it helps you