## Answer :

Quadratic functions with real coefficients have solutions that come in conjugate pairs if the solutions are complex numbers. The conjugate of a complex number [tex]\( a + bi \)[/tex] is [tex]\( a - bi \)[/tex].

Given:

One solution is [tex]\( -4 + 7i \)[/tex].

Using the concept that the complex conjugate of this solution must also be a solution, we find that the other solution must be:

[tex]\[ -4 - 7i \][/tex]

Now we match this with the given options:

A. Function [tex]\( h \)[/tex] has no other solutions.

- This is incorrect because quadratic functions of degree 2 always have two solutions.

B. The other solution to function [tex]\( h \)[/tex] is [tex]\( -4 - 77 \)[/tex].

- This is incorrect because the correct conjugate solution involves the imaginary part, not a real number alone.

C. The other solution to function [tex]\( h \)[/tex] is [tex]\( 4 - 7i \)[/tex].

- This is incorrect because it incorrectly changes the real part of the given solution.

D. The other solution to function [tex]\( h \)[/tex] is [tex]\( -4 - 7i \)[/tex].

- This is correct because it is the conjugate of the given solution [tex]\( -4 + 7i \)[/tex].

Thus, the correct answer is:

[tex]\[ \boxed{4} \][/tex]