Question

One of the roots of equation 5m² + 2m + k = 0 is $\frac{-7}{5}$ . Complete the following activity to find the value of 'k'.

Answer 1

$\boxed{\frac{-7}{5}}$ is a root of the quadratic equation 5m² + 2m + k = 0.
∴ Put m = $\frac{-7}{5}$ in the equation.
$$\begin{gathered} 5\times {\boxed{\frac{-7}{5}}}^2+2\times \boxed{\frac{-7}{5}}+k=0 \\ \boxed{\frac{49}{5}}+\boxed{\frac{-14}{5}}+k=0 \\ \boxed{7}+k=0 \\ k=\boxed{-7} \end{gathered}$$