Question

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

Answer 1

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

∴ Put m = `(-7)/5` in the equation.   

5 × `((-7)/5)^2 + 2 xx (-7)/5 + k = 0`

`cancel(5) xx 49/(cancel(5) xx 5) + 2 xx (-7)/5 + k = 0`

`49/5 + (-14)/5 + k = 0`

`(49 - 14)/5 + k = 0`

`35/5 + k = 0`
7 + k = 0
k = - 7