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Question
One of the roots of 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 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
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