Equation with Opposite Roots:
To find an equation whose roots are numerically equal but opposite in sign of the roots of \(2x^2 + 3x + 4 = 0\), we first need to determine the roots of the given equation.

Finding Roots of the Given Equation:
1. Use the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
2. Substitute \(a = 2\), \(b = 3\), and \(c = 4\) into the formula.
3. Calculate the discriminant: \(D = b^2 - 4ac = 3^2 - 4(2)(4) = 9 - 32 = -23\)
4. Since the discriminant is negative, the roots are complex.

Equation with Opposite Roots:
To find an equation with roots that are numerically equal but opposite in sign, we use the fact that if \(r\) is a root of a quadratic equation, then \(-r\) is also a root.
1. Let the roots of the new equation be \(r\) and \(-r\).
2. The sum of roots, \(r + (-r)\), is 0.
3. The product of roots, \(r(-r)\), is \(-r^2\).
4. The equation with roots \(r\) and \(-r\) is of the form \(x^2 - (sum of roots)x + product of roots = 0\).
5. Substituting the values, the required equation is \(x^2 - 0x - r^2 = x^2 - r^2 = 0\).
Therefore, the equation whose roots are numerically equal but opposite in sign of the roots of \(2x^2 + 3x + 4 = 0\) is \(x^2 - r^2 = 0\).