If one root of $5x^{2}+13x+k=0$ is the reciprocal of the other root, then find the value of $k$.
Given: One root of $5x^{2}+13x+k=0$ is the reciprocal of the other root.
To do: To find the value of $k$.
Solution:
Let $\alpha$ is one root of the given polynomial.
It is given that other zero is Reciprocal the one zero.
So,
Other zero$=\frac{1}{\alpha}$.
Given polynomial is $5x^{2}+13x+k=0$.
Here,
coefficient of $( x^{2})=A=5$
coefficient of $( x)=B=x$
And, constant term $=C=k$.
Product of zeroes $=\frac{C}{A}$
$\alpha\times\frac{1}{\alpha}=\frac{k}{5}$
$1=\frac{k}{5}$
$k=5$
Then, $k=5$.
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