Question

If one root of the polynomial $f\left(x\right)=5x^2+13x+k$ is reciprocal of the other,then find the value of k

Answer 1

$f\left(x\right)=5x^2+13x+k$

let root be α

then 2^nd root= 1/α

Sum of root = -b/α

$\alpha +\frac{1}{\alpha }=\frac{-13}{5}$

$\frac{{\alpha }^2+1}{\alpha }=\frac{-13}{5}$

product $=c/\alpha$

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

$5=k$