Explanation:

Given:
- Quadratic polynomial: \(f(x) = kx^2 + 4x + 4\)
- Zeros: \(\alpha\) and \(\beta\)
- Sum of squares of zeros: \(\alpha^2 + \beta^2 = 24\)

Using Sum and Product of Zeros:
- The sum of zeros, \(\alpha + \beta\), can be found using the formula: \(\alpha + \beta = -\frac{b}{a}\), where \(a\) and \(b\) are the coefficients of the quadratic polynomial.
- The product of zeros, \(\alpha \beta\), can be found using the formula: \(\alpha \beta = \frac{c}{a}\), where \(c\) is the constant term of the quadratic polynomial.

Given Quadratic Polynomial:
- Coefficients: \(a = k\), \(b = 4\), \(c = 4\)

Finding Sum and Product of Zeros:
- \(\alpha + \beta = -\frac{4}{k}\)
- \(\alpha \beta = \frac{4}{k}\)

Given Condition:
- \(\alpha^2 + \beta^2 = 24\)

Using Sum and Product of Zeros Formulas:
- \((\alpha + \beta)^2 = \alpha^2 + 2\alpha\beta + \beta^2\)
- Substitute the values of \(\alpha + \beta\), \(\alpha \beta\), and \(\alpha^2 + \beta^2\).
- Solve for \(k\) to find the value of the sum of squares of zeros.

Conclusion:
- By substituting the given values and solving the equations, the value of \(k\) can be determined to satisfy the condition \(\alpha^2 + \beta^2 = 24\).