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One of the roots of equation 5m2 + 2m + k = 0 is \(-7\over5\) .Complete the following activity to find the value of ’k’.

Solution : ......... is a root of quadratic equation 5m2 + 2m + k = 0

Put m = ......... in the equation.

5 * .........^{2 }+ 2 * ......... + k=0

.........+.........+ k = 0

.........+ k = 0

k =.........

Sol. \(-7\over5\) is a root of quadratic equation 5m^{2} + 2m + k = 0

∴ Put m = \(-7\over5\) in the equation.

5 ×\(({-7\over5})^2\) + 2 × \(-7\over5\) + k = 0

∴ \(49\over 5\) + \(({-14\over 5})\) + k = 0

∴ \(49 – 14\over 5\) + k = 0

∴ \(35\over 5\) + k = 0

∴ 7 + k = 0

∴ k = –7