Question

One of the roots of the equation $5m^2+2m+k=0is\frac{-7}{5}$. Find the value of $k$

Answer 1

$5m^2+2m+k=0$

Since one of the roots is $\frac{-7}{5}$

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

$\Rightarrow 5\left(\frac{49}{25}\right)-\frac{14}{5}+k=0$

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

$\Rightarrow k=-7$

Hence, the answer is $-7.$