Question

Find $k$ if $m=\frac{-7}{5}$ is a root of the quadratic equation $5m^2+2m+k=0$

Answer 1

Since $m$ is a root of $5m^2+2m+k=0$, thus it must satify the equation.

Therefore,

$5{\left(\frac{-7}{5}\right)}^2+2\left(\frac{-7}{5}\right)+k=0$

$\frac{49}{5}-\frac{14}{5}+k=0$

$\Rightarrow k=\frac{14-49}{5}=\frac{-35}{5}=-7$

Hence the value of $k$ is $-7$.