Explanation:

- Equation I is: \( 2x^2 + 7x + k = 0 \). The sum of the roots of a quadratic equation \( ax^2 + bx + c = 0 \) is given by \(-b/a\).

- With \( a = 2 \), \( b = 7 \), the sum of roots for equation I is \(-7/2 = -3.5\).

- Equation II is: \( (ay + b)^2 = 0 \). This implies \( ay + b = 0 \), leading to one root: \( y = -b/a \).

- We know the smallest root of Equation I is -2. Thus, the sum of roots is \(-2 + \text{larger root}\).

- The larger root also satisfies Equation II. But only one root exists: \( y = -b/a \).

- Using the quadratic sum property, find the larger root: \(-2 + \text{larger root} = -3.5\).

- So, the sum of the roots of Equation I is \(-3.5\).

Option 3, -3.5 is correct.

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