Question

If one root of $5x^2+13x+k=0$ is the reciprocal of the other root, then find value of $k$.

Answer 1

Let one root of the given that other zero is Reciprocal the one zero.

So,

Other zero$=1$/Alpa.

Given polynomial is $5x^2+13x+k=0$.

Here,

$A$=coefficient of $x^2$

$B$=coefficient of $x$

And,$C$=constant term.

Product of zeroes =$C/A$

Alpha $\times$1/Alpha $=K/5$

$1=K/5$

$K=5$

Then,

We get $k=5$.