Answered

Select the correct answer.

One solution to a quadratic function, [tex]\( h \)[/tex], is given:
[tex]\[ -4 + 7i \][/tex]

Which statement is true?

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].



Answer :

GinnyAnswer
To determine the correct solution, let's analyze the given quadratic function characteristics and properties.

1. For any quadratic function with real coefficients, if one of the solutions is a complex number, it is guaranteed that the other solution will be the complex conjugate of the given solution.

2. The given solution is [tex]\( -4 + 7i \)[/tex].

3. The complex conjugate of a complex number [tex]\( a + bi \)[/tex] is [tex]\( a - bi \)[/tex]. Here, [tex]\( a = -4 \)[/tex] and [tex]\( b = 7 \)[/tex], making the complex conjugate [tex]\( -4 - 7i \)[/tex].

Therefore, since the quadratic function has real coefficients, the other solution must also be a complex conjugate of the given solution [tex]\( -4 + 7i \)[/tex].

Thus, the correct answer is:
[tex]\[ \text{B. The other solution to function } h \text{ is } -4-7i. \][/tex]