One of the roots of the quadratic equation `5x^(2) + 2x+ k = 0 ` is `- ( 7 )/( 5)`. Complete the following activity to find the value of k.
`- ( 7)/( 5)` is the root of the quadratic equation `5 x^(2) + 2x + k = 0 `.
`:.` Substitute `x = - ( 7)/( 5) ` in the equation
`:. 5 xx square + 2 xx square + k = 0 `
`:. square - square + k = 0 `
`:. square + k = 0 `
`:. k = square `

Explanation

To find the value of \( k \) in the quadratic equation \( 5x^2 + 2x + k = 0 \) given that one of the roots is \( -\frac{7}{5} \), we can follow these steps:

### Step 1: Substitute the root into the equation
Since \( -\frac{7}{5} \) is a root, we substitute \( x = -\frac{7}{5} \) into the equation:

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