To find the value of \( b \) in the equation \( x^2 + bx - 55 = 0 \) such that the solutions are \( -11 \) and \( 5 \), we can use Vieta's formulas. According to Vieta's formulas for the roots of a quadratic equation \( ax^2 + bx + c = 0 \):
- The sum of the roots \( r_1 + r_2 = -\frac{b}{a} \)
- The product of the roots \( r_1 \cdot r_2 = \frac{c}{a} \)
In this case, we have:
- The roots \( r_1 = -11 \) and \( r_2 = 5 \)
- The product of the roots \( r_1 \cdot r_2 = -11 \cdot 5 = -55 \)
- The sum of the roots \( r_1 + r_2 = -11 + 5 = -6 \)
From the product of the roots, we can see that \( c = -55 \), which is consistent with the equation provided.
Now using the sum of the roots to find \( b \):
\[ r_1 + r_2 = -6 = -\frac{b}{1} \]
This simplifies to:
\[ b = 6 \]
Thus, the value of \( b \) is \( 6 \).
So the correct answer is: A. 6.