Question

What should be the value of b in x2+bx−55=0
so that its solutions are −11
and 5? (1 point)
Responses

6
6

−16
negative 16

−6
negative 6

16

Answer 1

To find the value of \( b \) in the quadratic equation \( x^2 + bx - 55 = 0 \) given that the solutions are \( -11 \) and \( 5 \), we can use Vieta's formulas.

According to Vieta's formulas, for a quadratic equation of the form \( x^2 + bx + c = 0 \):
- The sum of the roots \( r_1 + r_2 = -b \)
- The product of the roots \( r_1 \cdot r_2 = c \)

In our case, the roots are \( r_1 = -11 \) and \( r_2 = 5 \).

1. **Calculate the sum of the roots:**
\[
-11 + 5 = -6
\]
According to Vieta's, this gives us:
\[
-b = -6 \quad \Rightarrow \quad b = 6
\]

2. **Calculate the product of the roots:**
\[
-11 \cdot 5 = -55
\]
This verifies the constant term \( c = -55 \).

Thus, the value of \( b \) that results in the roots of \( -11 \) and \( 5 \) for the equation \( x^2 + bx - 55 = 0 \) is:

\[
\boxed{6}
\]