Question

One of the roots of the quadratic equation 5m² + 2m + k = 0 is `(-7)/5`. Complete the following activity to find the value of ‘k’.

Solution:

`(-7)/5` is a root of quadratic equation 5m² + 2m + k = 0.

∴ put m = `(-7)/5` in the equation.

∴ 5 × `square^2` + 2 × `square` +  k = 0

`square + square` + k = 0

`square` + k = 0

∴ k = `square`

Answer 1

`(-7)/5` is a root of quadratic equation 5m² + 2m + k = 0.

∴ put m = `(-7)/5` in the equation.

∴ 5 × \[\boxed{\left(\frac{{-7}}{5}\right)^2}\] + 2 × \[\boxed{\frac{{-7}}{5}}\] +  k = 0

\[\boxed{\frac{{49}}{5}}\]  + \[\boxed{\frac{{-14}}{5}}\] + k = 0

\[\boxed{7}\] + k = 0

∴ k = \[\boxed{-7}\]