To find the value of \( b \) in the quadratic equation \( x^2 + bx - 55 = 0 \) given that its solutions are \( -11 \) and \( 5 \), we can use Vieta's formulas. According to Vieta's formulas, for a quadratic equation \( ax^2 + bx + c = 0 \), the sum of the solutions \( r_1 + r_2 \) is given by \( -\frac{b}{a} \) and the product of the solutions \( r_1 \cdot r_2 \) is given by \( \frac{c}{a} \).
-
Sum of the roots: \[ r_1 + r_2 = -11 + 5 = -6 \] According to Vieta's: \[ -\frac{b}{1} = -6 \implies b = 6 \]
-
Product of the roots: \[ r_1 \cdot r_2 = -11 \cdot 5 = -55 \] According to Vieta's: \[ \frac{-55}{1} = -55 \] This condition is satisfied with the given roots.
Thus, the value of \( b \) should be \( 6 \).
Therefore, the answer is: 6