Let's solve this step by step to determine the correct answer.
We are given one solution to the quadratic function [tex]\( h \)[/tex]:
[tex]\[ -4 + 7i \][/tex]
### Step 1: Identify the nature of the given solution
The given solution is a complex number. For quadratic functions with real coefficients, the solutions appear in conjugate pairs. This means if [tex]\( a + bi \)[/tex] is a solution, then [tex]\( a - bi \)[/tex] must also be a solution.
### Step 2: Find the conjugate of the given solution
The conjugate of a complex number [tex]\( a + bi \)[/tex] is [tex]\( a - bi \)[/tex]. Here, our complex number is [tex]\( -4 + 7i \)[/tex].
- Real part ([tex]\( a \)[/tex]): [tex]\(-4\)[/tex]
- Imaginary part ([tex]\( bi \)[/tex]): [tex]\(7i\)[/tex]
The conjugate will keep the real part the same and change the sign of the imaginary part:
[tex]\[ -4 - 7i \][/tex]
### Step 3: Match the conjugate to the options given
Now we need to match this conjugate solution with the options provided:
A. Function [tex]\( h \)[/tex] has no other solutions.
B. The other solution to function [tex]\( h \)[/tex] is [tex]\( -4 - 7i \)[/tex].
C. The other solution to function [tex]\( h \)[/tex] is [tex]\( 4 - 7i \)[/tex].
D. The other solution to function [tex]\( h \)[/tex] is [tex]\( 4 + 7i \)[/tex].
Option B states that the other solution is [tex]\( -4 - 7i \)[/tex], which matches our conjugate.
### Conclusion
The correct answer is:
[tex]\[ \boxed{\text{B. The other solution to function } h \text{ is } -4-7 i.} \][/tex]
